%I #31 Apr 29 2019 05:22:34

%S 1,1,4,1,10,76,1,40,1120,67840,1,136,16576,4212736,1073790976,1,544,

%T 263680,268779520,274882625536,281475530358784,1,2080,4197376,

%U 17184194560,70368756760576,288230393868451840,1180591620768950910976

%N Triangle read by rows: T(n,m) is the number of pattern classes in the (n,m)-rectangular grid with 4 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 Burnside's orbit-counting lemma.

%H María Merino, <a href="/A283433/b283433.txt">Rows n=0..41 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) = (4^(m*n) + 3*4^(m*n/2))/4;

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

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

%F for odd n and m: T(n,m) = (4^(m*n) + 4^((m*n+n)/2) + 4^((m*n+m)/2) + 4^((m*n+1)/2))/4.

%e Triangle begins:

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

%e n\m | 0 1 2 3 4 5

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

%e 0 | 1

%e 1 | 1 4

%e 2 | 1 10 76

%e 3 | 1 40 1120 67840

%e 4 | 1 136 16576 4212736 1073790976

%e 5 | 1 544 263680 268779520 274882625536 281475530358784

%e ...

%Y Cf. A225910, A283432.

%K nonn,tabl

%O 0,3

%A _María Merino_, Imanol Unanue, _Yosu Yurramendi_, May 15 2017