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A252778
Number of ways of n-coloring the square grid graph G_(3,3) such that no rectangle exists with sides parallel to the axes having all 4 corners of the same color.
5
0, 0, 156, 14298, 228984, 1821420, 9676020, 39328086, 131914608, 382726584, 991134540, 2342199090, 5133181416, 10561434468, 20593784484, 38341504110, 68569332960, 118371718896, 198054533628, 322265959434, 511426049880, 793510636380, 1206251784276
OFFSET
0,3
COMMENTS
The square grid graph G_(3,3) has 9 vertices, 12 edges and 9 rectangles with sides parallel to the axes.
a(4) = A200045(3,3) = 228984.
LINKS
Eric Weisstein's World of Mathematics, Grid Graph
FORMULA
a(n) = n*(n-1)*(n^7+n^6+n^5-8*n^4-8*n^3+4*n^2+22*n-14).
G.f.: 6 *x^2 *(11*x^7 +92*x^6 +2829*x^5 +13850*x^4 +26045*x^3 +15504*x^2 +2123*x +26) / (x-1)^10.
MAPLE
a:= n-> (((((n^3-9)*n^2+12)*n+18)*n-36)*n+14)*n:
seq(a(n), n=0..30);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Dec 21 2014
STATUS
approved