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.

A286392 Number of inequivalent n X n matrices over an alphabet of size 6 under action of dihedral group of the square D_4.

This page as a plain text file.
%I A286392 #46 Apr 15 2021 15:18:28
%S A286392 1,6,231,1284066,352654485156,3553786240466361696,
%T A286392 1289303099816839265917858176,16839193280515921004090301582258640896,
%U A286392 7917535832871659713272867459049024690729209839616
%N A286392 Number of inequivalent n X n matrices over an alphabet of size 6 under action of dihedral group of the square D_4.
%C A286392 Computed using Burnside's orbit-counting lemma.
%H A286392 María Merino, <a href="/A286392/b286392.txt">Table of n, a(n) for n = 0..35</a>
%H A286392 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 A286392 a(n) = (1/8)*(6^(n^2) + 2*6^(n^2/4) + 3*6^(n^2/2) + 2*6^((n^2 + n)/2)) if n is even;
%F A286392 a(n) = (1/8)*(6^(n^2) + 2*6^((n^2 + 3)/4) + 6^((n^2 + 1)/2)  + 4*6^((n^2 + n)/2)) if n is odd.
%t A286392 Table[1/8*(6^(n^2) + 2*6^((n^2 + 3 #)/4) + (3 - 2 #)*6^((n^2 + #)/2) + (2 + 2 #)*6^((n^2 + n)/2)) &@ Boole[OddQ@ n], {n, 10}] (* _Michael De Vlieger_, May 08 2017 *)
%Y A286392 Column k=6 of A343097.
%Y A286392 Cf. A054247, A054739, A054751, A054752.
%K A286392 nonn,easy
%O A286392 0,2
%A A286392 _María Merino_, Imanol Unanue, _Yosu Yurramendi_, May 08 2017