A048452 Starting from generation 5 add previous and next term yielding generation 6.

56, 127, 181, 276, 339, 453, 540, 656, 780, 888, 1036, 1146, 1290, 1420, 1550, 1704, 1826, 1984, 2112, 2254, 2404, 2542, 2708, 2856, 3014, 3160, 3300, 3460, 3588, 3806, 3922, 4190, 4290, 4556, 4656, 4886, 5012, 5208, 5352, 5546, 5670, 5888, 5986, 6224