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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, 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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified September 22 16:41 EDT 2019. Contains 327311 sequences. (Running on oeis4.)