cp's OEIS Frontend

A286921 Triangle read by rows: T(n,m) is the number of pattern classes in the (n,m)-rectangular grid with 10 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 A286921 #24 Apr 29 2019 08:25:05
%S A286921 1,1,10,1,55,2575,1,550,253000,250525000,1,5050,25007500,250025500000,
%T A286921 2500000075000000,1,50500,2500300000,250002775000000,
%U A286921 25000000255000000000,2500000000502500000000000,1,500500,250000750000,250000250500000000,250000000000750000000000,250000000000250500000000000000,250000000000000000750000000000000000
%N A286921 Triangle read by rows: T(n,m) is the number of pattern classes in the (n,m)-rectangular grid with 10 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 A286921 Computed using Burnsides orbit-counting lemma.
%H A286921 María Merino, <a href="/A286921/b286921.txt">Rows n=0..32 of triangle, flattened</a>
%H A286921 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 A286921 For even n and m: T(n,m) = (10^(m*n) + 3*10^(m*n/2))/4;
%F A286921 for even n and odd m: T(n,m) = (10^(m*n) + 10^((m*n+n)/2) + 2*10^(m*n/2))/4;
%F A286921 for odd n and even m: T(n,m) = (10^(m*n) + 10^((m*n+m)/2) + 2*10^(m*n/2))/4;
%F A286921 for odd n and m: T(n,m) = (10^(m*n) + 10^((m*n+n)/2) + 10^((m*n+m)/2) + 10^((m*n+1)/2))/4.
%e A286921 Triangle begins:
%e A286921 ==============================================================
%e A286921 n\m |   0   1      2          3              4
%e A286921 ----|---------------------------------------------------------
%e A286921 0   |   1
%e A286921 1   |   1   10
%e A286921 2   |   1   55     2575
%e A286921 3   |   1   550    253000     250525000
%e A286921 4   |   1   5050   25007500   250025500000   2500000075000000
%e A286921 ...
%Y A286921 Cf. A225910, A283432, A283433, A283434, A286893, A286895, A286919, A286920.
%K A286921 nonn,tabl
%O A286921 0,3
%A A286921 _María Merino_, Imanol Unanue, _Yosu Yurramendi_, May 16 2017