A153903 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 4 X 4 X 4 subtriangle.

1, 2, 2, 3, 3, 7, 10, 21, 34, 88, 150, 421, 807, 2708, 6019, 22444, 58037, 245472, 706322, 3364913, 10967191, 59955069, 222028350, 1374087876, 5812458172, 40846719268, 195779164954, 1558347753536, 8466932734756, 76665491618022, 472779311230382