A286895 Triangle read by rows: T(n,m) is the number of pattern classes in the (n,m)-rectangular grid with 7 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, 7, 1, 28, 637, 1, 196, 30184, 10151428, 1, 1225, 1443001, 3461821825, 8308236966001, 1, 8575, 70656628, 1186972525900, 19948070175962425, 335267157313994232775, 1, 58996, 3460410037, 407106879976216, 47895307855522569001, 5634835073082541702198396, 662932711464914589254954278237

Offset

0,3

Comments

Computed using Burnside's 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) = (7^(m*n) + 3*7^(m*n/2))/4;

for even n and odd m: T(n,m) = (7^(m*n) + 7^((m*n+n)/2) + 2*7^(m*n/2))/4;

for odd n and even m: T(n,m) = (7^(m*n) + 7^((m*n+m)/2) + 2*7^(m*n/2))/4;

for odd n and m: T(n,m) = (7^(m*n) + 7^((m*n+n)/2) + 7^((m*n+m)/2) + 7^((m*n+1)/2))/4.

Example

Triangle begins:
============================================================================
n\m |  0  1    2        3             4                 5
----|-----------------------------------------------------------------------
0   |  1
1   |  1  7
2   |  1  28   637
3   |  1  196  30184    10151428
4   |  1  1225 1443001  3461821825    8308236966001
5   |  1  8575 70656628 1186972525900 19948070175962425 335267157313994232775
...

Crossrefs

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

Sequence in context: A282917 A050301 A146996 * A083994 A301731 A228498

Adjacent sequences: A286892 A286893 A286894 * A286896 A286897 A286898

Keyword

nonn,tabl

Author

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

Status

approved