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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.
4
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
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
KEYWORD
nonn,tabl
AUTHOR
María Merino, Imanol Unanue, Yosu Yurramendi, May 15 2017
STATUS
approved