cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A054739 Number of inequivalent n X n matrices over GF(3) under action of dihedral group of the square D_4.

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