A153987 Number of planar n X n X n binary triangular grids with mirror symmetry about one altitude with every one adjacent to exactly 2 other ones.

1, 1, 2, 3, 5, 12, 33, 97, 381, 1490, 7757, 42774, 307960, 2294754, 22718581, 231171797, 3121763126, 43651298703, 807916379400, 15440457456928, 391605380566734, 10243338678890245, 355535039683009851