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.

1, 1, 10, 1, 55, 2575, 1, 550, 253000, 250525000, 1, 5050, 25007500, 250025500000, 2500000075000000, 1, 50500, 2500300000, 250002775000000, 25000000255000000000, 2500000000502500000000000, 1, 500500, 250000750000, 250000250500000000, 250000000000750000000000, 250000000000250500000000000000, 250000000000000000750000000000000000

Offset: 0

Author

María Merino, Imanol Unanue, Yosu Yurramendi, May 16 2017

Keywords

• nonn
• tabl

Comments

Computed using Burnsides orbit-counting lemma.

Examples

			Triangle begins:
==============================================================
n\m |   0   1      2          3              4
----|---------------------------------------------------------
0   |   1
1   |   1   10
2   |   1   55     2575
3   |   1   550    253000     250525000
4   |   1   5050   25007500   250025500000   2500000075000000
...
		

Links

• María Merino, Rows n=0..32 of triangle, flattened
• M. Merino and I. Unanue, Counting squared grid patterns with Pólya Theory, EKAIA, 34 (2018), 289-316 (in Basque).

Crossrefs

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

Formula

For even n and m: T(n,m) = (10^(m*n) + 3*10^(m*n/2))/4;

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

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

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.