A350891 Number of colorings of an n X n X n grid with at most two interchangeable colors under rotational and reflectional symmetry.

1, 14, 1426144, 192153653985253376, 443075998594975502964308746247864320, 1097003038214137361436646127021900210236442855769266059743330304

Offset

1,2

Links

Kacper Blachut, Table of n, a(n) for n = 1..14

Formula

a(2n) = (2^(8*n^3) + 3*2^(2*n^3 + 3) + 13*2^(4*n^3 + 1) + 2^((4*n^3 + 2*n + 12)/3) + 2^((8*n^3 + 4*n + 9)/3) + 3*2^(4*n^3 + 2*n^2 + 1))/96.

a(2n+1) = (2^(8*n^3 + 12*n^2 + 6*n + 1) + 6*2^(2*n^3 + 3*n^2 + 4*n + 1) + 9*2^(4*n^3 + 6*n^2 + 4*n + 1) + 8*2^((8*n^3 + 12*n^2 + 10*n + 3)/3) + 9*2^(4*n^3 + 8*n^2 + 5*n + 1) + 6*2^(2*n^3 + 3*n^2 + 2*n + 1) + 2^(4*n^3 + 6*n^2 + 3*n + 1) + 8*2^((4*n^3 + 6*n^2 + 5*n + 3)/3))/96.

Crossrefs

Cf. A182044.

Sequence in context: A159430 A013800 A368692 * A347626 A013870 A195898

Adjacent sequences: A350888 A350889 A350890 * A350892 A350893 A350894

Keyword

nonn

Author

Kacper Blachut, Jan 21 2022

Status

approved