A153897 Number of planar n X n X n binary triangular grids with mirror symmetry about one altitude with no more than 1 one in any 2 X 2 X 2 subtriangle.

1, 2, 2, 6, 10, 38, 84, 462, 1454, 10978, 47966, 507832, 3102956, 45765610, 389928206, 8030198134, 95507073248, 2744133148026, 45539464036516, 1826082647001502, 42290971759195390, 2366417546297792380, 76478152220819322380