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A283434 Triangle read by rows: T(n,m) is the number of pattern classes in the (n,m)-rectangular grid with 5 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. 6
1, 1, 5, 1, 15, 175, 1, 75, 4125, 496875, 1, 325, 98125, 61140625, 38147265625, 1, 1625, 2446875, 7632421875, 23841923828125, 74505821533203125, 1, 7875, 61046875, 953736328125, 14901161376953125, 232830644622802734375, 3637978807094573974609375 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Computed using Burnside's orbit-counting lemma.

LINKS

María Merino, Rows n=0..38 of triangle, flattened

FORMULA

For even n and m: T(n,m) = (5^(m*n) + 3*5^(m*n/2))/4;

for even n and odd m: T(n,m) = (5^(m*n) + 5^((m*n+n)/2) + 2*5^(m*n/2))/4;

for odd n and even m: T(n,m) = (5^(m*n) + 5^((m*n+m)/2) + 2*5^(m*n/2))/4;

for odd n and m: T(n,m) = (5^(m*n) + 5^((m*n+n)/2) + 5^((m*n+m)/2) + 5^((m*n+1)/2))/4.

EXAMPLE

Triangle begins:

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

n\m |   0   1      2         3            4                5

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

0   |   1

1   |   1   5

2   |   1   15     175

3   |   1   75     4125      496875

4   |   1   325    98125     61140625     38147265625

5   |   1   1625   2446875   7632421875   23841923828125   74505821533203125

...

CROSSREFS

Cf. A225910, A283432, A283433.

Sequence in context: A157385 A157397 A157405 * A019429 A221364 A211805

Adjacent sequences:  A283431 A283432 A283433 * A283435 A283436 A283437

KEYWORD

nonn,tabl

AUTHOR

María Merino, Imanol Unanue, Yosu Yurramendi, May 15 2017

STATUS

approved

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Last modified October 20 17:39 EDT 2017. Contains 293648 sequences.