A286921 - OEIS

%I #24 Apr 29 2019 08:25:05

%S 1,1,10,1,55,2575,1,550,253000,250525000,1,5050,25007500,250025500000,

%T 2500000075000000,1,50500,2500300000,250002775000000,

%U 25000000255000000000,2500000000502500000000000,1,500500,250000750000,250000250500000000,250000000000750000000000,250000000000250500000000000000,250000000000000000750000000000000000

%N 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 Computed using Burnsides orbit-counting lemma.

%H María Merino, <a href="/A286921/b286921.txt">Rows n=0..32 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) = (10^(m*n) + 3*10^(m*n/2))/4;

%F for even n and odd m: T(n,m) = (10^(m*n) + 10^((m*n+n)/2) + 2*10^(m*n/2))/4;

%F for odd n and even m: T(n,m) = (10^(m*n) + 10^((m*n+m)/2) + 2*10^(m*n/2))/4;

%F 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 Triangle begins:

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

%e n\m |   0   1      2          3              4

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

%e 0   |   1

%e 1   |   1   10

%e 2   |   1   55     2575

%e 3   |   1   550    253000     250525000

%e 4   |   1   5050   25007500   250025500000   2500000075000000

%e ...

%Y Cf. A225910, A283432, A283433, A283434, A286893, A286895, A286919, A286920.

%K nonn,tabl

%O 0,3

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