A153982 Number of planar n X n X n binary triangular grids symmetric under 120 degree rotation with every one adjacent to exactly 1 other one.

1, 1, 1, 1, 3, 6, 11, 30, 72, 201, 747, 2553, 10966, 58566, 287270, 1751705, 13247679, 91522060, 788765512, 8490555128, 84280981845, 1040689637617, 15976611935513, 225667587813248, 3966856029530488, 86787076062074170, 1745622351406501121