A153915 Number of planar n X n X n binary triangular grids with mirror symmetry about one altitude with no more than 2 ones in any 4 X 4 X 4 subtriangle.

1, 2, 3, 6, 8, 23, 56, 204, 561, 2634, 9589, 57271, 263195, 2051213, 12518144, 126095265, 984855718, 12768865644, 128552370071, 2154052520419, 28007473176570, 606579298687089, 10205582308897812, 285438654888054564