A350891 - OEIS

%I #12 Mar 05 2022 01:22:33

%S 1,14,1426144,192153653985253376,443075998594975502964308746247864320,

%T 1097003038214137361436646127021900210236442855769266059743330304

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

%H Kacper Blachut, <a href="/A350891/b350891.txt">Table of n, a(n) for n = 1..14</a>

%F 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.

%F 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.

%Y Cf. A182044.

%K nonn

%O 1,2

%A _Kacper Blachut_, Jan 21 2022