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A283432 Triangle read by rows: T(n,m) is the number of pattern classes in the (n,m)-rectangular grid with 3 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. 8
1, 1, 3, 1, 6, 27, 1, 18, 216, 5346, 1, 45, 1701, 134865, 10766601, 1, 135, 15066, 3608550, 871858485, 211829725395, 1, 378, 133407, 96997824, 70607782701, 51472887053238, 37523659114815147, 1, 1134, 1198476, 2616461190, 5719211266905, 12507889858389450, 27354747358715650524, 59824832319304600777362 (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..46 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) = (3^(m*n) + 3*3^(m*n/2))/4;

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

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

for odd n and m: T(n,m) = (3^(m*n) + 3^((m*n+n)/2) + 3^((m*n+m)/2) + 3^((m*n+1)/2))/4.

EXAMPLE

Triangle begins:

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

n\ m |   0  1     2      3         4           5

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

0    |   1

1    |   1  3

2    |   1  6     27

3    |   1  18    216    5346

4    |   1  45    1701   134865    10766601

5    |   1  135   15066  3608550   871858485   211829725395

...

CROSSREFS

Cf. A225910.

Sequence in context: A175291 A156363 A221929 * A157866 A221852 A025230

Adjacent sequences:  A283429 A283430 A283431 * A283433 A283434 A283435

KEYWORD

nonn,tabl

AUTHOR

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

STATUS

approved

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Last modified November 29 02:34 EST 2020. Contains 338756 sequences. (Running on oeis4.)