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.

A286919 Triangle read by rows: T(n,m) is the number of pattern classes in the (n,m)-rectangular grid with 8 colors and n>=m, two patterns are in the same class if one of them can be obtained by a reflection or 180-degree rotation of the other.

This page as a plain text file.
%I A286919 #26 Apr 29 2019 06:16:03
%S A286919 1,1,8,1,36,1072,1,288,66816,33693696,1,2080,4197376,17184194560,
%T A286919 70368756760576,1,16640,268517376,8796399206400,288230393868451840,
%U A286919 9444732983468915425280,1,131328,17180065792,4503616874348544,1180591620768950910976,309485009825866260538195968,81129638414606695206587887255552
%N A286919 Triangle read by rows: T(n,m) is the number of pattern classes in the (n,m)-rectangular grid with 8 colors and n>=m, two patterns are in the same class if one of them can be obtained by a reflection or 180-degree rotation of the other.
%C A286919 Computed using Burnsides orbit-counting lemma.
%H A286919 María Merino, <a href="/A286919/b286919.txt">Rows n=0..35 of triangle, flattened</a>
%H A286919 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 A286919 For even n and m: T(n,m) = (8^(m*n) + 3*8^(m*n/2))/4;
%F A286919 for even n and odd m: T(n,m) = (8^(m*n) + 8^((m*n+n)/2) + 2*8^(m*n/2))/4;
%F A286919 for odd n and even m: T(n,m) = (8^(m*n) + 8^((m*n+m)/2) + 2*8^(m*n/2))/4;
%F A286919 for odd n and m: T(n,m) = (8^(m*n) + 8^((m*n+n)/2) + 8^((m*n+m)/2) + 8^((m*n+1)/2))/4.
%e A286919 Triangle begins:
%e A286919 ========================================================
%e A286919 n\m |   0   1      2        3             4
%e A286919 ----|---------------------------------------------------
%e A286919 0   |   1
%e A286919 1   |   1   8
%e A286919 2   |   1   36     1072
%e A286919 3   |   1   288    66816    33693696
%e A286919 4   |   1   2080   4197376  17184194560   70368756760576
%e A286919 ...
%Y A286919 Cf. A225910,  A283432, A283433, A283434, A286893, A286895.
%K A286919 nonn,tabl
%O A286919 0,3
%A A286919 _María Merino_, Imanol Unanue, _Yosu Yurramendi_, May 16 2017