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

0,3

Comments

Computed using Burnsides orbit-counting lemma.

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).

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.

Example

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
...

Crossrefs

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

Sequence in context: A146537 A050304 A143471 * A009209 A009227 A305996

Adjacent sequences: A286918 A286919 A286920 * A286922 A286923 A286924

Keyword

nonn,tabl

Author

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

Status

approved