cp's OEIS Frontend

A286920 Triangle read by rows: T(n,m) is the number of pattern classes in the (n,m)-rectangular grid with 9 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.

%I A286920 #24 Apr 29 2019 08:24:58
%S A286920 1,1,9,1,45,1701,1,405,134865,97135605,1,3321,10766601,70618411521,
%T A286920 463255079498001,1,29889,871858485,51473762336565,3039416437115008521,
%U A286920 179474497026544179696969,1,266085,70607782701,37523729625344145,19941610769429949618201,10597789568841677482963905405,5632099886234793715531013441442501
%N A286920 Triangle read by rows: T(n,m) is the number of pattern classes in the (n,m)-rectangular grid with 9 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 A286920 Computed using Burnsides orbit-counting lemma.
%H A286920 María Merino, <a href="/A286920/b286920.txt">Rows n=0..33 of triangle, flattened</a>
%H A286920 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 A286920 For even n and m: T(n,m) = (9^(m*n) + 3*9^(m*n/2))/4;
%F A286920 for even n and odd m: T(n,m) = (9^(m*n) + 9^((m*n+n)/2) + 2*9^(m*n/2))/4;
%F A286920 for odd n and even m: T(n,m) = (9^(m*n) + 9^((m*n+m)/2) + 2*9^(m*n/2))/4;
%F A286920 for odd n and m: T(n,m) = (9^(m*n) + 9^((m*n+n)/2) + 9^((m*n+m)/2) + 9^((m*n+1)/2))/4.
%e A286920 Triangle begins:
%e A286920 ==========================================================
%e A286920 n\m |   0   1     2         3              4
%e A286920 ----|-----------------------------------------------------
%e A286920 0   |   1
%e A286920 1   |   1   9
%e A286920 2   |   1   45    1701
%e A286920 3   |   1   405   134865    97135605
%e A286920 4   |   1   3321  10766601  70618411521    463255079498001
%e A286920 ...
%Y A286920 Cf. A225910, A283432, A283433, A283434, A286893, A286895, A286919.
%K A286920 nonn,tabl
%O A286920 0,3
%A A286920 _María Merino_, Imanol Unanue, _Yosu Yurramendi_, May 16 2017