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A153986

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

1, 1, 2, 2, 2, 4, 9, 15, 37, 88, 191, 729, 2246, 6555, 31434, 144150, 601688, 3970089, 24322158, 135488789, 1251604698, 10410417129, 79632436378, 997602199170, 11483571472544, 120898733308159, 2073714604283068, 32605974669636948