%I #25 Dec 11 2023 18:18:09
%S 1,2,6,140,16456,8390720,17179934976,140737496748032,
%T 4611686019501162496,604462909807864344215552,
%U 316912650057057631849169289216,664613997892457937028364283517337600,5575186299632655785385110159782842147536896,187072209578355573530071668259090783437390809661440
%N Number of 2-colorings of an n X n grid, up to rotational symmetry.
%C Cycle index = 1/4(s_1^(n^2)+ 2 s_4^floor(n^2/4)s_1^(n mod 2)+s_2^floor(n^2/2)s_1^(n mod 2)). - _Geoffrey Critzer_, Oct 28 2011
%H Andrew Howroyd, <a href="/A047937/b047937.txt">Table of n, a(n) for n = 0..50</a>
%H Peter Kagey, <a href="/A047937/a047937.pdf">Illustration of a(3)=140</a>
%H Peter Kagey and William Keehn, <a href="https://arxiv.org/abs/2311.13072">Counting tilings of the n X m grid, cylinder, and torus</a>, arXiv:2311.13072 [math.CO], 2023.
%F a(n) = (m^(n^2) + 2*m^((n^2 + 3*(n mod 2))/4) + m^((n^2 + (n mod 2))/2))/4, with m = 2.
%e a(2)=6 from
%e 00 10 11 10 11 11
%e 00 00 00 01 10 11
%t Table[(2^(n^2)+2*2^Floor[n^2/4]*2^Mod[n,2]+2^Floor[n^2/2]*2^Mod[n,2])/4,{n,0,10}] (* _Geoffrey Critzer_, Oct 28 2011 *)
%Y Column k=2 of A343095.
%Y Other columns are A047938, A047939, A047940, A047941, A047942, A047943, A047944, A047945.
%Y Cf. A054247.
%K nonn,easy,nice
%O 0,2
%A _Rob Pratt_
%E Terms a(12) and beyond from _Andrew Howroyd_, Apr 14 2021