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%I #38 Apr 15 2021 16:03:22
%S 1,9,1035,48700845,231628411446741,89737248564744874067889,
%T 2816049943117424212512789695666175,
%U 7158021121277935153545945911617993395398302485,1473773072217322896440109113309952350877179744639518847951721
%N Number of inequivalent n X n matrices over GF(9) under action of dihedral group of the square D_4.
%C Burnside's orbit-counting lemma.
%H María Merino, <a href="/A286396/b286396.txt">Table of n, a(n) for n = 0..32</a>
%H 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 a(n) = (1/8)*(9^(n^2) + 2*9^(n^2/4) + 3*9^(n^2/2) + 2*9^((n^2 + n)/2)) if n is even;
%F a(n) = (1/8)*(9^(n^2) + 2*9^((n^2 + 3)/4) + 9^((n^2 + 1)/2) + 4*9^((n^2 + n)/2)) if n is odd.
%t Table[1/8*(9^(n^2) + 2*9^((n^2 + 3 #)/4) + (3 - 2 #)*9^((n^2 + #)/2) + (2 + 2 #)*9^((n^2 + n)/2)) &@ Boole@ OddQ@ n, {n, 0, 7}] (* _Michael De Vlieger_, May 12 2017 *)
%Y Column k=9 of A343097.
%Y Cf. A054247, A054739, A054751, A054752, A286392, A286393, A286394.
%K nonn
%O 0,2
%A _María Merino_, Imanol Unanue, _Yosu Yurramendi_, May 08 2017
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