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%I #22 Apr 15 2021 15:27:19
%S 1,3,21,2862,5398083,105918450471,18761832172500795,
%T 29912416165371498901002,429210477536602279123636967061,
%U 55428311030379722725246681652572022523,64422190091501416379601522735200323789074174081,673878862467911703904942451533575765568815772023224550102
%N Number of inequivalent n X n matrices over GF(3) under action of dihedral group of the square D_4.
%H Andrew Howroyd, <a href="/A054739/b054739.txt">Table of n, a(n) for n = 0..25</a>
%F a(n) = (1/8)*(3^(n^2) + 2*3^(n^2/4) + 3*3^(n^2/2) + 2*3^((n^2+n)/2)) if n is even;
%F a(n) = (1/8)*(3^(n^2) + 2*3^((n^2+3)/4) + 3^((n^2+1)/2) + 4*3^((n^2+n)/2)) if n is odd. [corrected by _Chris Hallstrom_, Mar 22 2021]
%t Join[{1, 3}, Table[CycleIndexPolynomial[
%t GraphData[{"Grid", {n, n}}, "AutomorphismGroup"],
%t Table[Subscript[s, i], {i, 1, 4}]] /.
%t Table[Subscript[s, i] -> 3, {i, 1, 4}], {n, 2, 10}]]
%t (* _Geoffrey Critzer_, Aug 09 2016 *)
%Y Column k=3 of A343097.
%Y Cf. A054247.
%K easy,nonn
%O 0,2
%A _Vladeta Jovovic_, May 15 2000
%E Terms a(10) and beyond from _Andrew Howroyd_, Apr 15 2021
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