%I #26 Apr 29 2019 06:16:03

%S 1,1,8,1,36,1072,1,288,66816,33693696,1,2080,4197376,17184194560,

%T 70368756760576,1,16640,268517376,8796399206400,288230393868451840,

%U 9444732983468915425280,1,131328,17180065792,4503616874348544,1180591620768950910976,309485009825866260538195968,81129638414606695206587887255552

%N 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 Computed using Burnsides orbit-counting lemma.

%H María Merino, <a href="/A286919/b286919.txt">Rows n=0..35 of triangle, flattened</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 For even n and m: T(n,m) = (8^(m*n) + 3*8^(m*n/2))/4;

%F for even n and odd m: T(n,m) = (8^(m*n) + 8^((m*n+n)/2) + 2*8^(m*n/2))/4;

%F for odd n and even m: T(n,m) = (8^(m*n) + 8^((m*n+m)/2) + 2*8^(m*n/2))/4;

%F 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 Triangle begins:

%e ========================================================

%e n\m | 0 1 2 3 4

%e ----|---------------------------------------------------

%e 0 | 1

%e 1 | 1 8

%e 2 | 1 36 1072

%e 3 | 1 288 66816 33693696

%e 4 | 1 2080 4197376 17184194560 70368756760576

%e ...

%Y Cf. A225910, A283432, A283433, A283434, A286893, A286895.

%K nonn,tabl

%O 0,3

%A _María Merino_, Imanol Unanue, _Yosu Yurramendi_, May 16 2017