A153921 Number of planar n X n X n binary triangular grids with mirror symmetry about one altitude with no more than 3 ones in any 3 X 3 X 3 subtriangle.

1, 2, 4, 10, 28, 148, 714, 6039, 49623, 697824, 9570390, 228608398, 5268376882, 211052632687, 8181458661819, 550685739585810, 35868897568521948, 4059582510922093828, 444431993377350866570, 84536428851931450778591