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A286919 Triangle read by rows: T(n,m) is the number of pattern classes in the (n,m)-rectangular grid with 8 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. 3
1, 1, 8, 1, 36, 1072, 1, 288, 66816, 33693696, 1, 2080, 4197376, 17184194560, 70368756760576, 1, 16640, 268517376, 8796399206400, 288230393868451840, 9444732983468915425280, 1, 131328, 17180065792, 4503616874348544, 1180591620768950910976, 309485009825866260538195968, 81129638414606695206587887255552 (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..35 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) = (8^(m*n) + 3*8^(m*n/2))/4;

for even n and odd m: T(n,m) = (8^(m*n) + 8^((m*n+n)/2) + 2*8^(m*n/2))/4;

for odd n and even m: T(n,m) = (8^(m*n) + 8^((m*n+m)/2) + 2*8^(m*n/2))/4;

for odd n and m: T(n,m) = (8^(m*n) + 8^((m*n+n)/2) + 8^((m*n+m)/2) + 8^((m*n+1)/2))/4.

EXAMPLE

Triangle begins:

========================================================

n\m |   0   1      2        3             4

----|---------------------------------------------------

0   |   1

1   |   1   8

2   |   1   36     1072

3   |   1   288    66816    33693696

4   |   1   2080   4197376  17184194560   70368756760576

...

CROSSREFS

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

Sequence in context: A224997 A275790 A050302 * A286260 A226374 A050401

Adjacent sequences:  A286916 A286917 A286918 * A286920 A286921 A286922

KEYWORD

nonn,tabl

AUTHOR

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

STATUS

approved

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Last modified September 15 18:47 EDT 2019. Contains 327083 sequences. (Running on oeis4.)