A153943 Number of planar n X n X n binary triangular grids symmetric both under 120 degree rotation and reflection with no more than 5 ones in any 4 X 4 X 4 subtriangle.

1, 2, 2, 3, 4, 8, 14, 49, 79, 253, 741, 2335, 6399, 37905, 102246, 593203, 2884877, 16569870, 80670284, 832584915, 3998999249, 40528587997, 352270529241, 3516190442125, 29997079375598, 543310308646601, 4559849026688799