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%I #10 Dec 23 2014 19:26:10
%S 0,0,144,13932,226224,1809360,9637200,39225564,131679072,382238784,
%T 990202320,2340528300,5130339984,10556808912,20586528144,38330476380,
%U 68553028800,118348187904,198021287952,322219869804,511363229040,793426309200,1206140143824
%N 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.
%C The square grid graph G_(3,3) has 9 vertices, 12 edges and 10 rectangles.
%H Alois P. Heinz, <a href="/A252779/b252779.txt">Table of n, a(n) for n = 0..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>
%F a(n) = n*(n-1)^2*(n^6+2*n^5+3*n^4-6*n^3-15*n^2-4*n+12).
%F 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.
%p a:= n-> (((((n^3-10)*n^2+20)*n+5)*n-28)*n+12)*n:
%p seq(a(n), n=0..30);
%Y Cf. A252778, A252780, A252839.
%K nonn,easy
%O 0,3
%A _Alois P. Heinz_, Dec 21 2014
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