A286893 Triangle read by rows: T(n,m) is the number of pattern classes in the (n,m)-rectangular grid with 6 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, 6, 1, 21, 351, 1, 126, 12096, 2544696, 1, 666, 420876, 544638816, 705278736576, 1, 3996, 15132096, 117564302016, 914040184444416, 7107572245840091136, 1, 23436, 544230576, 25390538401536, 1184595336212990976, 55268479955808421134336, 2578606199622710056510488576

Offset

0,3

Comments

Computed using Burnside's orbit-counting lemma.

Links

María Merino, Rows n=0..36 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) = (6^(m*n) + 3*6^(m*n/2))/4;

for even n and odd m: T(n,m) = (6^(m*n) + 6^((m*n+n)/2) + 2*6^(m*n/2))/4;

for odd n and even m: T(n,m) = (6^(m*n) + 6^((m*n+m)/2) + 2*6^(m*n/2))/4;

for odd n and m: T(n,m) = (6^(m*n) + 6^((m*n+n)/2) + 6^((m*n+m)/2) + 6^((m*n+1)/2))/4.

Example

Triangle begins:
============================================================================
n\m |  0  1     2         3             4                5
----|-----------------------------------------------------------------------
0   |  1
1   |  1  6
2   |  1  21    351
3   |  1  126   12096     2544696
4   |  1  666   420876    544638816     705278736576
5   |  1  3996  15132096  117564302016  914040184444416  7107572245840091136
...

Crossrefs

Cf. A225910, A283432, A283433, A283434.

Sequence in context: A120666 A050300 A185678 * A118394 A365372 A278906

Adjacent sequences: A286890 A286891 A286892 * A286894 A286895 A286896

Keyword

nonn,tabl

Author

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

Status

approved