Calculando la Serie de Lucas con Java - Usando la Clase Big Decimal java.math.BigDecimal

Hola a todos, hoy vamos a realizar una modificación al programa con el que calculamos la Serie de Fibonacci usando la clase BigDecimal con el objetivo de poder calcular la Serie de Lucas. 

Esta serie, tiene la misma definición de la de Fibonacci, en la que el término siguiente se calcula sumando los dos términos anteriores. A diferencia de la de Fibonacci, la Serie de Lucas inicia con el 1 y el 3 (no con el 1 y 1 como es en el caso de Fibonacci).

Ajustemos entonces nuestro programa y lo ejecutamos para ver el resultado:

Vamos a reescribir el programa y cambiamos los valores de inicio en las lineas correspondientes:

Y creamos una aplicación para probarla:

Y si la ejecutamos, tenemos el el término L20 de la serie de Lucas es: 15.127.

Calculemos entonces, el término L100000 y veamos el resultado:

5.807.978.471.268.136.356.022.506.800.460.238.722.059.782.866.612.699.348.136.955.104.001.418.008.563.425.084.641.321.277.250.355.647.449.603.564.683.409.215.162.118.484.650.256.921.564.370.578.556.318.398.595.105.127.156.867.299.660.448.890.911.782.356.304.024.720.050.718.417.052.928.190.905.977.554.736.172.855.213.336.814.644.978.512.232.593.721.392.107.802.767.415.323.187.813.600.974.609.480.450.463.929.039.303.204.879.432.864.765.387.089.401.756.120.952.848.848.992.064.921.744.921.180.652.369.202.227.142.567.482.818.563.764.871.120.477.741.088.224.233.712.017.141.785.120.972.681.119.724.122.117.240.468.390.772.312.159.243.180.225.970.289.217.549.071.032.963.572.690.369.322.418.027.493.545.265.076.214.327.333.074.776.218.086.942.785.486.950.687.811.848.288.670.712.738.288.303.310.684.062.262.189.381.183.672.904.767.720.820.938.317.385.903.325.173.637.674.930.445.091.613.668.094.605.279.828.824.146.794.765.739.303.488.326.614.854.133.586.796.918.303.989.829.975.513.415.250.071.253.939.403.624.850.677.488.106.218.063.868.232.128.609.532.176.962.019.600.651.781.129.629.159.740.010.322.043.631.677.119.683.126.959.963.563.865.782.234.668.229.807.452.214.015.382.631.284.740.069.408.261.540.394.181.142.742.279.118.094.005.576.753.237.663.068.077.004.145.948.532.581.684.399.582.501.269.012.366.599.731.671.936.756.681.565.850.994.941.696.483.169.767.524.598.893.814.781.225.265.720.854.416.268.832.015.874.710.088.752.454.824.480.456.513.470.040.286.259.736.649.723.548.428.137.410.084.094.755.077.869.156.823.406.987.604.197.284.239.356.120.261.591.928.288.752.217.399.906.735.032.724.118.378.957.719.876.568.242.837.912.580.268.608.528.476.006.773.289.965.147.260.156.618.681.699.748.955.359.994.377.284.151.998.013.703.388.685.059.319.083.387.122.981.053.573.773.530.987.929.477.207.793.075.086.219.534.983.703.759.423.652.148.356.860.342.672.141.684.022.645.507.275.775.493.638.852.788.750.059.667.643.933.241.002.164.303.167.071.638.111.456.259.611.845.578.790.795.523.628.256.213.660.401.644.261.098.507.402.415.309.945.890.183.269.607.446.242.172.925.510.071.602.829.227.598.983.114.072.210.425.964.586.218.406.486.160.738.594.892.825.198.330.530.788.126.443.364.393.188.992.236.200.501.669.653.458.273.042.200.279.412.727.563.185.371.380.300.436.431.969.452.078.344.052.832.943.004.256.687.408.668.103.767.689.148.358.023.328.229.974.211.396.458.786.331.206.101.142.066.114.975.679.608.123.694.361.358.713.091.474.438.881.037.874.237.340.594.795.553.143.671.873.783.869.440.108.416.029.448.596.596.005.246.254.873.270.022.143.468.709.189.711.161.232.558.957.146.462.066.584.809.061.428.249.291.041.623.897.806.599.361.608.137.141.182.292.181.937.980.019.854.970.564.486.919.248.985.051.397.240.052.109.779.714.356.066.900.021.678.208.500.792.366.415.927.639.927.366.176.409.239.336.719.608.033.375.870.014.383.432.153.782.266.451.461.190.592.311.875.306.713.934.654.994.218.258.903.447.444.035.358.243.024.869.250.241.036.052.016.614.051.331.361.407.829.064.327.092.168.085.909.269.013.797.459.014.996.017.457.021.415.186.784.742.688.920.890.953.837.137.795.503.574.177.172.429.057.548.174.631.098.532.854.244.301.706.050.655.185.078.476.961.347.103.874.440.622.892.002.826.875.350.568.980.387.558.919.927.221.289.680.591.081.879.274.805.730.956.206.415.655.608.464.464.314.043.137.973.749.169.356.480.788.476.480.115.190.250.420.808.016.571.718.638.077.522.609.215.835.458.703.516.767.775.089.552.429.444.659.373.293.844.205.748.009.133.519.449.382.248.410.415.139.205.740.283.512.368.466.904.306.978.082.022.949.442.397.289.444.820.105.031.433.703.146.659.150.872.977.571.363.040.733.563.831.148.623.936.489.890.772.752.815.453.488.445.382.317.139.497.663.017.207.076.774.270.783.820.873.820.602.117.922.993.840.315.412.184.819.686.824.239.639.499.380.684.536.506.387.286.927.667.518.212.501.546.932.840.452.182.140.473.054.906.281.530.121.731.958.602.279.621.613.265.430.553.502.999.135.385.539.777.683.742.862.381.000.072.336.044.441.577.223.663.482.401.646.013.012.906.680.784.372.873.158.514.846.904.871.497.947.021.519.867.502.249.289.836.990.419.934.868.059.855.723.922.733.082.621.554.800.643.687.240.173.333.989.087.768.004.144.323.330.265.075.034.679.022.831.157.910.907.254.009.208.444.602.955.380.508.617.095.966.163.197.215.154.017.570.371.811.827.667.120.028.749.067.075.903.089.118.380.039.384.079.329.296.037.318.574.263.013.629.395.571.876.529.469.496.117.976.148.941.364.016.403.687.738.388.592.094.678.312.668.381.427.166.762.713.801.797.619.924.616.803.980.783.649.190.006.534.131.667.041.465.274.732.876.461.008.747.691.197.583.175.890.782.885.857.325.796.399.893.519.510.217.872.403.230.385.064.427.959.801.164.188.016.371.815.037.607.690.061.066.661.530.946.765.461.788.109.262.605.792.083.236.432.787.324.438.720.705.214.829.182.532.224.471.558.033.954.810.565.754.401.982.650.494.771.036.462.585.335.067.544.769.923.196.732.012.877.660.223.580.041.067.019.002.608.282.065.016.731.509.331.672.435.238.111.976.593.404.400.548.067.689.194.015.296.643.868.378.024.153.296.261.590.825.907.862.297.744.966.136.899.393.488.183.557.518.757.898.471.932.497.363.061.962.867.648.872.434.522.506.795.083.816.464.167.540.894.952.903.088.354.551.412.824.369.009.913.519.659.604.217.432.873.454.201.672.846.111.566.618.811.912.313.751.129.127.402.724.030.644.618.437.448.760.959.186.638.218.736.470.516.427.895.601.437.490.882.155.338.218.948.565.632.909.455.242.999.410.177.698.795.819.971.448.006.203.519.648.634.799.246.864.997.976.393.980.430.185.139.464.532.116.832.904.006.314.630.141.827.544.979.144.677.280.378.541.820.468.702.054.125.099.437.935.210.131.690.954.644.515.349.569.481.056.626.165.445.475.889.935.653.247.890.145.600.519.600.059.775.763.972.663.972.528.417.822.354.541.104.066.768.516.460.393.831.555.793.160.091.238.423.428.378.544.369.517.209.802.636.214.640.982.822.511.474.723.801.237.565.967.793.084.006.787.408.516.388.399.802.590.722.423.826.081.823.378.884.852.098.736.853.636.104.045.733.325.112.132.871.048.369.323.029.802.771.407.835.333.950.322.036.763.462.367.344.752.191.856.390.136.930.439.044.084.254.927.739.541.627.639.696.280.538.476.842.255.933.721.153.910.633.763.532.503.515.764.968.823.446.429.110.158.254.583.614.491.825.554.602.003.765.735.018.844.143.932.633.460.226.050.501.106.969.937.083.793.546.618.493.462.063.636.677.076.268.977.152.622.632.482.074.910.261.997.855.338.233.304.046.023.818.241.142.016.465.164.679.994.055.737.885.776.939.527.090.570.975.479.655.923.698.323.821.248.117.231.481.629.106.955.313.197.315.839.939.209.604.928.896.226.289.113.800.363.606.223.606.655.596.459.306.475.198.327.681.303.483.644.061.665.775.080.396.672.888.782.709.143.125.974.698.670.854.463.911.886.185.679.182.797.589.685.248.474.556.614.637.797.970.153.376.965.043.177.250.369.651.553.927.038.989.922.030.309.108.373.619.945.454.011.156.857.469.876.954.183.645.952.216.828.616.483.742.769.121.090.963.532.949.269.880.940.957.231.777.009.056.111.920.494.897.005.449.201.577.143.883.965.380.088.986.199.334.651.570.057.495.107.848.629.768.286.676.197.925.142.061.240.399.420.150.194.253.853.637.047.408.418.397.929.086.236.893.618.343.282.795.441.093.897.679.596.829.261.688.109.379.834.378.006.143.893.289.259.377.319.390.816.976.278.169.686.446.673.903.582.214.305.667.232.675.474.002.095.842.645.760.149.624.857.102.271.792.779.521.882.831.549.243.900.159.884.472.653.182.187.417.275.150.684.733.018.604.169.260.521.389.793.791.786.455.540.007.850.719.862.324.549.269.537.266.065.095.711.198.684.490.219.956.150.965.041.634.218.854.679.075.095.917.858.474.868.572.865.909.996.578.328.771.062.874.430.039.875.512.492.831.497.913.066.073.215.781.761.966.818.872.884.149.251.660.444.864.979.931.934.676.227.903.656.575.448.398.728.023.108.205.530.410.991.652.329.678.341.361.576.950.601.131.797.009.360.708.577.932.085.971.087.783.645.691.840.199.752.754.921.398.971.443.614.382.272.391.412.603.948.661.043.463.520.795.652.590.985.186.360.663.686.910.701.304.435.663.012.690.072.960.173.221.876.088.789.183.376.353.606.421.106.708.202.234.107.586.414.268.542.449.546.156.817.764.934.747.658.480.459.076.339.347.947.473.767.667.577.983.131.897.821.565.090.474.179.602.663.541.435.106.515.973.801.478.676.540.497.832.552.903.104.401.447.884.709.278.839.517.027.815.262.663.199.522.029.933.826.518.525.278.262.493.293.673.769.193.498.317.525.790.696.250.038.878.375.639.862.322.837.844.824.778.257.540.247.163.593.038.935.313.720.079.312.966.312.983.117.665.370.182.703.605.208.010.689.546.847.690.055.391.455.587.497.670.223.110.952.368.204.617.700.265.978.171.440.209.317.956.807.775.012.623.341.213.641.304.586.607.237.015.688.125.112.057.509.111.996.095.940.467.732.878.332.754.497.084.643.760.734.337.601.071.052.034.425.850.918.323.319.563.897.099.172.417.251.849.963.815.405.129.194.108.467.798.488.064.419.584.087.711.532.838.964.834.707.560.656.485.924.562.960.958.885.778.946.887.091.035.145.953.605.589.645.594.123.296.124.776.882.541.804.155.726.774.704.468.997.045.659.826.603.524.796.722.237.467.170.871.198.157.673.261.368.537.910.746.284.695.518.448.999.905.987.796.171.029.537.355.055.086.296.567.195.539.268.499.066.207.257.048.567.034.184.400.657.549.469.348.749.790.504.295.914.895.835.810.670.240.224.193.506.315.015.561.255.149.578.771.947.419.136.298.358.630.495.742.034.143.956.520.033.609.493.150.458.326.649.671.705.281.992.247.249.085.833.575.957.319.173.635.291.588.936.280.371.042.874.579.697.738.021.142.793.137.873.732.342.080.390.935.929.945.491.305.082.969.182.208.058.660.032.890.877.101.398.684.608.990.486.977.137.850.971.269.557.200.784.214.582.038.218.539.412.578.867.396.002.776.206.107.464.925.988.317.675.581.366.128.505.155.119.012.733.853.429.135.005.409.684.469.489.700.137.750.913.396.423.592.350.327.618.956.914.403.032.608.676.319.141.022.396.530.903.282.818.690.942.409.272.028.484.982.661.858.907.570.248.006.474.686.362.801.593.611.460.755.200.073.693.701.827.673.024.330.636.542.103.193.343.906.441.487.066.490.438.359.939.628.623.060.390.623.590.092.061.529.555.840.135.042.550.130.349.265.616.965.946.855.561.010.655.290.451.611.352.111.159.243.879.900.233.007.426.732.332.050.669.259.235.287.804.395.115.402.167.482.303.549.805.544.670.617.673.017.098.011.226.869.909.807.566.873.012.694.908.402.050.694.858.158.022.521.259.213.539.937.557.306.012.170.414.932.404.065.436.063.597.780.433.656.121.855.358.402.993.205.144.681.520.321.978.272.086.686.343.146.390.581.466.804.220.200.961.884.829.487.986.378.315.236.037.749.271.952.434.218.810.645.176.861.525.772.086.451.805.117.055.400.013.067.698.193.372.904.802.678.701.840.815.696.657.318.348.375.810.056.798.981.000.098.316.914.535.833.543.416.700.635.040.675.439.707.853.771.682.181.280.083.528.965.821.539.478.173.867.126.033.504.637.694.963.389.916.535.959.480.944.457.455.200.710.320.235.044.495.961.768.019.950.928.392.460.248.757.109.361.213.291.369.834.388.205.451.575.062.974.012.030.477.852.846.795.694.282.355.728.332.919.931.743.880.014.182.709.803.668.179.269.605.183.783.881.836.120.317.245.003.770.985.728.197.403.718.637.014.512.541.010.893.407.927.200.394.967.982.933.515.345.881.337.665.426.856.573.845.467.605.435.334.310.635.688.752.326.896.236.377.275.189.424.612.582.424.748.993.111.479.935.662.908.682.923.630.861.989.696.307.612.836.166.134.703.585.270.282.060.263.241.601.258.601.097.021.951.556.076.025.874.620.659.997.520.614.897.782.891.218.351.517.255.708.913.175.943.940.492.302.555.985.767.583.494.710.227.932.421.058.870.590.313.970.345.825.326.009.125.617.680.095.511.836.525.647.287.419.132.792.227.561.781.642.244.311.150.693.806.373.334.429.986.706.867.117.098.283.628.795.509.638.906.834.171.376.108.789.833.289.403.716.571.774.390.365.812.975.121.941.529.890.347.969.556.439.194.619.043.024.303.723.781.090.147.881.649.470.192.622.375.522.093.722.982.418.822.774.007.617.611.201.431.296.963.126.934.595.429.129.251.215.539.784.503.279.441.194.071.172.678.220.377.167.768.180.042.845.554.667.346.084.932.859.433.534.813.370.133.725.251.541.169.925.845.417.172.176.590.177.349.363.680.471.880.017.220.671.947.351.037.412.752.592.480.112.508.164.104.251.370.940.697.334.736.498.257.665.171.113.418.770.129.013.416.119.214.884.981.254.527.969.187.911.148.048.626.884.243.932.546.618.129.295.096.690.909.148.781.568.405.817.542.916.593.751.460.344.606.207.381.011.463.187.172.319.756.156.956.482.180.839.433.721.688.961.877.659.019.196.026.226.803.384.190.383.455.519.318.955.527.405.301.934.285.001.323.122.781.378.356.526.715.502.858.793.842.955.557.062.156.385.719.660.849.417.577.686.131.301.463.146.663.442.098.225.575.754.558.320.562.957.617.479.228.399.017.614.063.098.799.417.712.874.879.528.327.708.174.770.046.552.261.771.333.648.596.494.446.343.973.858.906.413.612.271.322.425.830.651.343.170.051.367.582.511.049.147.008.956.167.637.683.511.946.384.589.013.958.453.987.871.705.795.836.768.468.499.171.803.720.899.583.221.805.904.698.766.075.578.172.776.462.181.144.564.815.668.048.036.736.108.484.231.188.267.752.216.732.233.436.677.991.123.454.160.454.278.617.781.575.862.358.140.997.257.403.266.546.640.432.067.889.128.381.842.436.673.972.393.274.406.938.095.208.142.335.710.245.046.926.042.662.198.154.645.604.945.976.484.673.266.192.580.856.628.250.448.850.888.167.915.242.432.108.290.443.544.583.810.774.757.786.037.564.689.006.925.313.313.019.281.460.344.590.529.994.146.626.232.866.625.700.903.393.064.525.047.448.940.412.319.188.786.793.443.630.146.813.746.204.616.025.539.630.695.361.049.114.006.278.892.861.711.291.528.746.219.995.448.934.526.584.679.531.985.258.563.858.411.347.825.224.039.503.445.107.921.786.704.218.939.235.987.143.759.047.482.764.671.891.423.748.440.987.072.650.801.437.639.382.609.192.643.353.739.371.390.029.498.340.901.638.351.716.042.001.295.381.929.187.461.409.843.395.345.462.645.153.721.910.961.093.217.330.874.364.068.861.014.031.956.705.201.433.647.389.755.851.767.503.017.148.765.367.116.666.755.298.233.964.112.048.699.843.732.676.243.328.168.245.058.788.019.447.884.716.021.239.064.403.354.460.136.589.350.006.912.299.064.283.438.949.228.438.637.027.264.543.019.571.341.088.165.832.858.622.259.508.411.653.330.528.701.583.390.399.491.001.708.160.163.842.815.438.981.291.684.466.215.403.104.177.424.331.581.309.981.457.570.349.709.625.292.776.175.174.381.546.626.292.601.034.481.125.369.458.718.987.502.274.029.560.541.469.596.695.008.066.206.005.585.190.597.330.251.542.372.801.899.720.855.178.952.494.318.156.500.043.540.054.157.593.715.107.998.271.742.135.011.571.768.333.645.083.961.100.137.255.524.784.199.301.701.820.337.546.052.585.972.529.100.947.791.100.243.355.446.517.736.964.488.137.571.914.516.688.819.708.233.053.088.358.038.229.031.409.065.902.214.173.757.562.333.752.535.143.898.621.197.786.791.880.593.784.915.824.899.371.732.249.765.440.199.600.642.516.170.078.673.050.315.633.512.877.078.075.139.020.546.052.915.930.427.854.964.474.761.572.408.059.381.889.105.160.234.298.166.537.349.545.078.855.515.200.149.712.215.546.080.354.617.322.857.804.174.898.747.173.094.803.295.513.060.222.614.983.773.078.467.445.502.137.096.626.050.632.383.715.676.815.519.178.670.108.159.501.560.771.310.852.798.960.312.689.757.147.574.761.595.783.609.177.792.963.043.170.088.841.580.767.936.355.605.941.365.950.672.314.537.199.081.463.091.532.129.703.823.020.832.061.165.501.973.669.449.993.387.070.924.501.909.872.848.750.906.725.757.290.435.122.884.516.369.994.801.977.042.270.007.855.948.481.413.005.920.872.973.983.102.442.625.929.490.701.108.727.090.795.019.244.582.323.281.486.730.269.002.450.084.821.530.589.714.862.000.428.147.101.651.244.788.340.804.569.058.899.176.203.692.274.469.767.996.908.291.697.920.735.960.440.941.994.802.943.187.743.015.972.432.996.773.438.608.084.447.066.654.792.537.400.294.906.512.818.959.083.444.613.350.882.607.501.817.556.601.053.432.938.870.891.044.039.390.992.666.713.681.701.677.458.334.976.732.199.535.386.351.251.469.459.005.943.823.186.875.569.279.282.560.944.537.182.324.838.171.890.742.657.302.757.396.776.218.070.740.004.056.842.956.198.081.269.797.705.218.057.556.063.438.072.019.454.056.420.312.679.743.425.709.696.769.153.924.000.530.379.150.328.434.914.290.718.315.960.566.789.328.205.825.251.938.087.043.798.205.097.027.787.191.265.987.579.927.093.883.420.511.776.992.390.704.947.217.494.351.536.190.295.203.238.043.073.519.143.940.585.500.419.229.669.401.302.690.703.332.715.818.664.135.203.569.586.710.200.384.984.943.594.673.018.186.604.214.960.089.658.202.644.151.818.635.048.395.649.486.674.957.499.210.642.146.139.029.280.365.909.870.284.777.165.991.205.986.298.261.914.627.632.830.960.028.362.198.165.006.631.344.822.044.167.722.360.395.440.987.957.566.326.708.119.459.217.744.390.889.016.910.768.807.700.492.182.590.780.872.851.920.179.649.478.846.918.408.702.280.241.144.957.314.409.998.609.222.698.166.829.562.604.848.314.019.902.694.113.985.175.415.692.620.686.485.922.721.084.007.964.234.946.236.994.116.415.705.284.335.383.090.177.823.681.264.206.363.536.191.730.416.325.213.933.752.415.655.947.680.286.622.338.266.145.043.982.845.508.563.457.619.238.665.382.941.025.127.919.123.534.277.104.429.320.359.492.648.298.247.978.179.160.066.583.879.825.108.963.512.449.801.714.329.818.739.076.312.929.800.911.550.706.074.778.186.433.647.012.942.992.110.717.382.229.021.229.993.378.580.068.964.407.879.783.381.018.429.097.508.504.924.620.967.162.493.401.781.228.976.338.900.772.903.043.560.801.316.614.783.292.572.895.488.940.670.818.262.631.397.839.339.283.626.590.467.489.759.358.206.182.792.004.823.222.643.270.468.929.294.175.843.886.149.560.834.066.657.989.252.888.905.310.513.209.004.986.575.448.657.837.186.136.843.838.688.956.281.735.726.314.956.868.594.113.183.114.200.572.348.109.144.387.577.949.648.720.163.142.626.564.705.670.741.514.871.172.203.159.061.518.096.761.109.245.266.514.714.383.731.128.857.519.095.087.091.190.689.828.317.867.849.713.218.781.815.075.440.664.660.539.643.212.515.804.575.427.766.515.772.642.338.145.361.881.023.311.545.528.816.986.842.738.713.037.314.258.998.580.099.450.658.618.051.604.360.864.624.035.582.262.814.263.565.881.470.044.644.002.615.543.642.566.768.504.005.903.480.688.329.154.370.616.902.445.358.261.723.708.141.035.611.984.901.299.468.824.168.452.777.820.593.004.372.190.328.265.200.850.193.827.700.744.347.730.130.136.549.989.658.353.644.991.875.161.777.311.447.510.545.818.042.421.462.829.741.890.751.896.150.434.745.874.413.654.444.586.968.481.024.074.399.260.288.201.286.162.668.698.267.792.173.923.415.011.357.708.991.959.594.345.564.456.227.706.036.757.623.727.537.051.250.659.661.442.864.031.435.751.385.703.851.072.686.942.866.745.082.264.864.504.689.899.547.043.281.898.669.561.708.259.395.078.288.199.054.817.582.578.793.586.843.582.644.601.307.931.552.403.289.215.982.540.998.112.279.765.352.553.668.716.459.896.178.429.241.289.164.177.656.042.358.155.067.954.142.050.514.346.617.251.317.610.552.251.506.640.394.377.093.117.223.865.433.036.595.306.122.433.363.436.676.724.466.409.604.379.556.685.704.013.633.094.691.052.421.067.324.779.238.591.554.993.200.340.515.015.830.441.173.862.916.295.632.551.054.342.912.803.772.289.680.427.965.176.153.682.390.852.180.254.752.624.820.450.994.658.647.991.248.638.210.402.691.945.534.157.354.280.101.874.021.529.227.607.869.349.247.339.422.279.120.338.278.522.031.185.468.852.984.362.491.433.779.303.258.147.701.226.336.991.258.758.948.347.000.724.033.667.106.257.168.660.137.274.172.932.880.705.350.259.579.638.860.850.284.053.450.013.139.357.812.535.697.375.288.840.550.475.216.444.483.796.413.679.270.615.754.060.241.917.025.313.969.580.833.142.885.280.331.647.154.568.859.485.234.753.410.638.867.401.025.467.809.751.336.529.632.554.139.489.167.054.790.513.459.589.524.459.316.889.767.605.471.761.962.844.511.574.117.653.492.598.459.771.052.261.942.844.246.291.079.588.993.601.639.110.511.002.517.761.276.990.674.061.009.711.132.886.791.809.557.230.632.388.539.467.475.862.119.957.899.190.866.022.272.642.741.887.958.671.967.448.601.375.060.233.392.372.657.104.509.950.704.727.244.608.724.670.020.575.008.785.701.592.666.222.158.224.073.246.900.247.567.115.243.181.339.191.682.148.528.555.422.721.047.071.773.443.952.914.525.395.497.954.329.991.777.667.120.889.320.498.924.128.198.499.868.014.896.935.961.162.625.532.056.513.500.165.622.649.231.659.146.009.647.745.280.199.396.097.318.678.589.389.580.703.411.718.531.578.748.148.436.515.802.931.338.158.979.507.752.584.563.238.809.070.636.966.174.473.673.929.693.968.645.557.710.139.988.016.344.709.970.678.995.401.381.864.443.899.867.961.890.898.904.009.105.006.743.753.900.044.922.201.061.297.357.665.667.236.872.362.807.246.332.315.252.563.869.208.962.944.082.101.510.494.199.256.755.350.591.646.721.328.833.850.737.260.319.488.359.518.137.541.264.061.247.384.093.371.056.949.183.103.445.772.275.417.749.268.475.776.345.086.331.391.281.117.705.917.039.595.881.582.826.741.210.272.982.543.130.998.170.811.853.195.936.784.180.690.641.902.179.999.074.606.456.698.823.029.067.411.398.505.367.235.150.431.905.946.496.439.263.764.403.271.369.007.115.210.820.376.579.227.564.081.203.001.924.801.443.311.474.871.154.055.290.622.806.041.811.498.412.927.228.853.097.159.223.150.620.679.554.825.469.631.172.194.406.960.447.185.804.658.322.672.928.500.229.689.628.902.024.021.769.378.361.453.533.984.930.767.637.287.221.122.674.049.079.891.395.441.220.455.801.966.609.238.320.427.719.338.305.769.869.628.197.721.881.242.699.915.043.112.888.256.100.983.507.874.571.348.704.861.611.714.387.451.230.885.895.131.367.854.017.847.335.879.227.268.660.958.676.484.985.741.439.494.396.485.533.484.605.494.928.254.812.071.597.546.702.533.623.319.708.176.963.375.998.967.789.352.343.100.298.129.710.210.807.863.279.259.544.372.830.692.038.726.767.604.245.469.915.746.486.690.032.578.327.379.552.734.468.696.472.235.425.466.449.886.639.875.056.034.317.041.854.387.221.595.939.174.623.814.381.368.352.414.776.611.138.277.809.659.052.447.480.798.191.431.460.785.736.255.525.381.274.630.604.730.579.757.206.691.806.182.716.799.572.127.597.979.287.271.032.691.729.310.081.612.147.645.955.906.459.567.426.512.064.217.934.372.462.578.021.001.489.363.944.893.719.205.868.834.170.433.360.620.561.153.266.091.678.164.849.450.445.577.861.288.526.841.589.452.735.880.906.122.427.612.324.738.678.724.752.143.212.399.070.172.941.393.628.940.189.916.041.295.471.350.490.900.937.064.648.116.836.844.807.934.052.886.044.974.390.575.553.005.075.836.219.593.882.916.950.410.849.059.908.343.586.736.813.248.499.770.841.731.727.129.400.587.477.461.326.705.213.856.456.314.771.711.653.862.880.017.526.833.658.630.291.771.700.353.770.244.283.792.514.980.830.357.374.270.148.396.898.803.510.520.119.126.431.086.586.778.722.124.891.554.799.525.708.455.959.518.017.559.527.671.994.878.032.722.556.312.573.309.084.776.394.822.166.092.013.216.710.009.021.357.914.307.289.440.229.306.164.713.251.376.101.359.750.423.236.094.531.031.856.636.838.792.696.758.169.173.196.242.163.887.372.673.317.449.046.389.800.330.571.254.637.187.014.523.882.859.513.219.607.329.486.376.927.134.091.918.046.699.666.872.567.794.441.193.179.677.627.853.110.074.335.379.211.141.836.584.309.219.810.139.256.273.017.827.686.072.781.913.894.232.792.274.763.828.990.613.771.690.514.101.591.085.852.991.439.393.183.914.464.555.912.925.115.692.898.946.101.794.161.877.924.314.974.034.127.712.267.710.986.954.028.971.095.987.127.559.488.314.069.706.084.269.246.240.220.462.149.478.423.163.579.745.198.671.948.183.705.282.223.219.660.758.713.798.396.215.613.608.459.057.528.216.351.940.420.112.233.824.925.764.921.625.392.457.743.470.700.813.176.860.160.143.102.430.133.207.207.375.908.409.092.432.038.082.783.560.595.233.630.793.329.061.127.693.030.893.189.269.922.622.961.238.508.052.149.615.469.185.031.229.974.105.979.797.945.694.479.637.694.450.673.856.757.120.004.841.092.680.900.242.353.136.137.701.996.794.470.441.896.289.617.210.937.222.103.072.719.140.068.323.270.442.336.943.894.697.592.056.207.732.752.867.174.658.555.677.006.870.136.739.060.460.685.036.469.282.705.151.544.882.602.013.349.901.869.725.813.947.038.696.883.782.083.358.759.520.438.723.581.461.266.417.334.058.179.453.354.552.838.249.077.706.166.627.538.242.470.533.284.904.919.285.876.084.901.616.442.510.609.294.598.897.804.039.766.651.563.225.598.677.693.777.649.956.256.426.104.979.150.405.084.715.701.186.179.006.625.343.954.299.506.563.806.405.838.377.295.337.431.511.295.234.439.514.693.485.782.015.764.670.041.346.953.021.129.430.307.067.879.605.629.346.014.005.857.691.042.840.750.622.798.745.976.785.262.329.078.981.770.455.312.936.531.694.163.467.839.954.791.374.364.536.831.891.648.126.137.660.147.433.155.841.973.749.675.058.039.598.480.781.478.942.630.323.783.578.193.763.264.547.610.416.126.551.026.204.277.066.446.639.400.273.107.814.258.996.368.348.120.905.066.218.643.491.512.659.695.363.206.949.258.977.294.797.703.924.874.290.857.239.024.039.730.836.797.114.894.827.804.693.707.575.027.121.289.591.162.652.564.130.506.457.904.381.520.560.328.729.541.339.765.967.122.045.359.303.656.521.573.615.636.174.304.074.149.851.045.906.989.204.818.336.487.922.065.689.394.586.449.777.677.352.733.192.680.787.190.749.176.968.429.485.884.280.781.336.048.555.510.162.303.154.029.437.627.912.542.818.737.924.212.821.382.558.992.666.835.258.748.823.928.773.561.569.261.211.376.429.104.722.118.535.102.239.075.506.849.768.607.802.452.668.469.011.626.684.022.457.501.017.342.349.319.429.026.646.441.079.519.096.978.942.928.612.848.205.228.411.450.197.035.082.091.407.660.799.244.325.988.507.582.195.366.430.832.074.814.762.830.353.018.504.716.172.852.526.222.362.588.237.336.439.196.730.707.609.750.611.079.688.111.583.815.787.403.649.617.943.179.725.489.904.291.937.262.001.918.995.316.428.384.625.366.723.538.360.857.683.510.613.381.370.767.145.730.885.979.926.219.926.338.577.606.819.175.940.027.841.667.060.395.720.672.788.996.746.732.868.429.171.551.360.735.234.547.240.717.784.217.636.655.439.331.069.025.696.229.842.307.459.004.414.057.144.794.800.573.053.247.114.821.634.907.209.740.145.689.533.268.207.099.593.155.342.173.644.054.477.095.706.725.665.816.453.865.078.036.433.550.679.878.112.775.933.755.094.090.581.350.261.521.119.766.288.649.050.269.668.134.210.735.064.556.023.400.710.424.511.734.279.548.559.089.549.052.416.345.447.190.891.996.894.123.944.220.276.035.593.908.471.514.959.789.110.901.788.352.031.260.001.715.366.209.494.343.238.468.481.161.437.468.137.604.428.517.811.895.509.193.615.124.962.018.442.986.970.008.443.529.857.407.908.605.856.536.869.829.177.022.543.494.107.998.883.571.715.586.215.737.636.406.852.966.638.151.162.684.210.752.413.396.537.132.487.884.379.102.029.634.723.960.026.346.140.854.829.382.166.050.991.828.999.906.626.568.182.729.623.648.484.308.102.188.227.960.820.355.475.852.398.303.483.605.866.744.658.433.593.166.088.820.674.375.014.435.985.426.184.141.019.975.355.646.735.791.967.594.180.985.629.067.583.341.086.878.193.806.790.218.997.754.091.104.068.570.142.437.704.071.748.242.972.592.613.190.212.076.372.110.047.515.567.253.463.027.329.458.105.883.426.164.215.878.109.684.223.767.142.582.731.796.699.132.810.934.228.201.914.721.525.589.317.613.662.074.127.783.658.186.227.398.322.263.772.302.024.658.304.033.080.985.646.800.007.289.511.769.782.401.306.306.387.491.374.912.733.850.584.290.912.823.853.526.261.240.553.256.298.769.248.018.616.900.883.046.469.492.124.130.006.465.316.892.829.901.128.910.714.632.157.750.191.196.525.051.176.260.768.487.751.700.043.379.840.165.741.901.326.366.544.876.966.462.395.611.459.757.473.481.259.362.008.472.893.428.017.083.605.115.719.243.938.344.302.351.026.406.844.186.726.618.638.522.930.849.191.968.403.216.320.580.176.642.632.401.951.165.507.224.466.045.780.121.317.251.196.531.203.882.566.364.243.004.082.161.352.370.557.738.701.239.944.394.787.516.109.557.886.621.440.883.077.734.133.156.905.788.861.246.678.828.762.595.658.224.422.198.488.840.836.423.181.578.677.984.476.878.718.061.082.022.161.203.529.764.821.597.059.303.847.402.451.379.477.857.726.676.584.685.986.328.127

A continuación, el código fuente:

package series;

import java.math.BigDecimal;
import java.text.DecimalFormat;

public class SerieLucasBD {

 private BigDecimal termino_inicial = BigDecimal.valueOf(1);
 private BigDecimal termino_siguiente = BigDecimal.valueOf(3);
 private BigDecimal termino_temp = BigDecimal.valueOf(0);

 private int total_terminos;

 private DecimalFormat format = new DecimalFormat("###,###");
 
 public SerieLucasBD(int total_terminos) {
  this.total_terminos = total_terminos;
 }

 public int getTotal_terminos() {
  return total_terminos;
 }

 public void setTotal_terminos(int total_terminos) {
  this.total_terminos = total_terminos;
  this.termino_inicial = BigDecimal.valueOf(1);
  this.termino_siguiente = BigDecimal.valueOf(3);
  this.termino_temp = BigDecimal.valueOf(0);
 }
 
 public void generarLucas() {
  
  int i = 0;
  
  for( i = 3 ; i <= total_terminos; i++) {
   
   //Ejecutar la suma de dos BigDecimal
   termino_temp = termino_inicial.add(termino_siguiente);
   termino_inicial = termino_siguiente;
   termino_siguiente = termino_temp;
  }
  
  System.out.println("" + (i-1) + " - " + format.format(termino_temp));  
  System.out.println("");
  
 }

}


package series;

public class SerieLucasBDTest {

 public static void main(String[] args) {
  // TODO Auto-generated method stub
  
  SerieLucasBD lucas = new SerieLucasBD(100000);
  lucas.generarLucas();
 }

}