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A252779
Number of ways of n-coloring the square grid graph G_(3,3) such that no rectangle exists having all 4 corners of the same color.
4
0, 0, 144, 13932, 226224, 1809360, 9637200, 39225564, 131679072, 382238784, 990202320, 2340528300, 5130339984, 10556808912, 20586528144, 38330476380, 68553028800, 118348187904, 198021287952, 322219869804, 511363229040, 793426309200, 1206140143824
OFFSET
0,3
COMMENTS
The square grid graph G_(3,3) has 9 vertices, 12 edges and 10 rectangles.
LINKS
Eric Weisstein's World of Mathematics, Grid Graph
FORMULA
a(n) = n*(n-1)^2*(n^6+2*n^5+3*n^4-6*n^3-15*n^2-4*n+12).
G.f.: 36 *x^2 *(x^7 +18*x^6 +481*x^5 +2280*x^4 +4355*x^3 +2594*x^2 +347*x+4) / (x-1)^10.
MAPLE
a:= n-> (((((n^3-10)*n^2+20)*n+5)*n-28)*n+12)*n:
seq(a(n), n=0..30);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Dec 21 2014
STATUS
approved