cp's OEIS Frontend

A287250 Number of inequivalent n X n matrices over GF(9) under action of dihedral group of the square D_4, with one-ninth each of 1's, 2's, 3's, 4's, 5's, 6's, 7's, 8's and 9's (ordered occurrences rounded up/down if n^2 != 0 mod 9).

%I A287250 #28 Aug 29 2020 02:34:52
%S A287250 1,1,1,45360,20432427120,1731557619792000000,
%T A287250 17601269260059379482191694720,
%U A287250 11370476506038919496334983007474778275840,944848320304251231447932170156537415535539635814400000,6641336088298446224006555306105706090482482272285249518936232000000000
%N A287250 Number of inequivalent n X n matrices over GF(9) under action of dihedral group of the square D_4, with one-ninth each of 1's, 2's, 3's, 4's, 5's, 6's, 7's, 8's and 9's (ordered occurrences rounded up/down if n^2 != 0 mod 9).
%C A287250 Computed using Polya's enumeration theorem for coloring.
%H A287250 María Merino, <a href="/A287250/b287250.txt">Table of n, a(n) for n = 0..31</a>
%H A287250 M. Merino and I. Unanue, <a href="https://doi.org/10.1387/ekaia.17851">Counting squared grid patterns with Pólya Theory</a>, EKAIA, 34 (2018), 289-316 (in Basque).
%F A287250 G.f.: g(x1,x2,x3,x4,x5,x6,x7,x8,x9) = (1/8)*(y1^(n^2)+2*y1^n*y2^((n^2-n)/2)+3*y2^(n^2/2)+2*y4^(n^2/4)) if n even and (1/8)*(y1^(n^2)+4*y1^n*y2^((n^2-n)/2)+y1*y2^((n^2-1)/2)+2*y1*y4^((n^2-1)/4)) if n odd, where coefficient correspond to y1=Sum_{i=1..9} x_i, y2=Sum_{i=1..9} x_i^2, y4=Sum_{i=1..9} x_i^4 and occurrences of numbers are ceiling(n^2/9) for the first k numbers and floor(n^2/9) for the last (9-k) numbers, if n^2 = k mod 9.
%e A287250 For n = 3 the a(3) = 45360 solutions are colorings of 3 X 3 matrices in 9 colors inequivalent under the action of D_4 with exactly 1 occurrence of each color (coefficient of x1^1 x2^1 x3^1 x4^1 x5^1 x6^1 x7^1 x8^1 x9^1).
%Y A287250 Cf. A286396, A082963,  A286447, A286525, A286526, A287239, A287245, A287249, A287261.
%K A287250 nonn
%O A287250 0,4
%A A287250 _María Merino_, Imanol Unanue, May 22 2017