A153988 Number of planar n X n X n binary triangular grids symmetric both under 120 degree rotation and reflection with every one adjacent to exactly 2 other ones.

1, 1, 2, 2, 2, 4, 7, 7, 19, 30, 41, 111, 242, 341, 1198, 2798, 5288, 19451, 58386, 113037, 552176, 1717743, 4407296, 22107632, 91701868, 243757707, 1626825070, 6947686128, 24465641567, 168345671664, 954487204861, 3466462776895