A286920 - OEIS

%I #24 Apr 29 2019 08:24:58

%S 1,1,9,1,45,1701,1,405,134865,97135605,1,3321,10766601,70618411521,

%T 463255079498001,1,29889,871858485,51473762336565,3039416437115008521,

%U 179474497026544179696969,1,266085,70607782701,37523729625344145,19941610769429949618201,10597789568841677482963905405,5632099886234793715531013441442501

%N 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 Computed using Burnsides orbit-counting lemma.

%H María Merino, <a href="/A286920/b286920.txt">Rows n=0..33 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) = (9^(m*n) + 3*9^(m*n/2))/4;

%F for even n and odd m: T(n,m) = (9^(m*n) + 9^((m*n+n)/2) + 2*9^(m*n/2))/4;

%F for odd n and even m: T(n,m) = (9^(m*n) + 9^((m*n+m)/2) + 2*9^(m*n/2))/4;

%F 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 Triangle begins:

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

%e n\m |   0   1     2         3              4

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

%e 0   |   1

%e 1   |   1   9

%e 2   |   1   45    1701

%e 3   |   1   405   134865    97135605

%e 4   |   1   3321  10766601  70618411521    463255079498001

%e ...

%Y Cf. A225910, A283432, A283433, A283434, A286893, A286895, A286919.

%K nonn,tabl

%O 0,3

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