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%I #30 Apr 29 2019 05:21:41
%S 1,1,5,1,15,175,1,75,4125,496875,1,325,98125,61140625,38147265625,1,
%T 1625,2446875,7632421875,23841923828125,74505821533203125,1,7875,
%U 61046875,953736328125,14901161376953125,232830644622802734375,3637978807094573974609375
%N Triangle read by rows: T(n,m) is the number of pattern classes in the (n,m)-rectangular grid with 5 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="/A283434/b283434.txt">Rows n=0..38 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) = (5^(m*n) + 3*5^(m*n/2))/4;
%F for even n and odd m: T(n,m) = (5^(m*n) + 5^((m*n+n)/2) + 2*5^(m*n/2))/4;
%F for odd n and even m: T(n,m) = (5^(m*n) + 5^((m*n+m)/2) + 2*5^(m*n/2))/4;
%F for odd n and m: T(n,m) = (5^(m*n) + 5^((m*n+n)/2) + 5^((m*n+m)/2) + 5^((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 5
%e 2 | 1 15 175
%e 3 | 1 75 4125 496875
%e 4 | 1 325 98125 61140625 38147265625
%e 5 | 1 1625 2446875 7632421875 23841923828125 74505821533203125
%e ...
%Y Cf. A225910, A283432, A283433.
%K nonn,tabl
%O 0,3
%A _María Merino_, Imanol Unanue, _Yosu Yurramendi_, May 15 2017
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