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.

A283433 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.

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%I A283433 #31 Apr 29 2019 05:22:34
%S A283433 1,1,4,1,10,76,1,40,1120,67840,1,136,16576,4212736,1073790976,1,544,
%T A283433 263680,268779520,274882625536,281475530358784,1,2080,4197376,
%U A283433 17184194560,70368756760576,288230393868451840,1180591620768950910976
%N A283433 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 A283433 Computed using Burnside's orbit-counting lemma.
%H A283433 María Merino, <a href="/A283433/b283433.txt">Rows n=0..41 of triangle, flattened</a>
%H A283433 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 A283433 For even n and m: T(n,m) = (4^(m*n) + 3*4^(m*n/2))/4;
%F A283433 for even n and odd m: T(n,m) = (4^(m*n) + 4^((m*n+n)/2) + 2*4^(m*n/2))/4;
%F A283433 for odd n and even m: T(n,m) = (4^(m*n) + 4^((m*n+m)/2) + 2*4^(m*n/2))/4;
%F A283433 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 A283433 Triangle begins:
%e A283433 =======================================================================
%e A283433 n\m |  0   1       2        3           4               5
%e A283433 ----|------------------------------------------------------------------
%e A283433 0   |  1
%e A283433 1   |  1    4
%e A283433 2   |  1    10     76
%e A283433 3   |  1    40     1120     67840
%e A283433 4   |  1    136    16576    4212736     1073790976
%e A283433 5   |  1    544    263680   268779520   274882625536    281475530358784
%e A283433 ...
%Y A283433 Cf. A225910, A283432.
%K A283433 nonn,tabl
%O A283433 0,3
%A A283433 _María Merino_, Imanol Unanue, _Yosu Yurramendi_, May 15 2017