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%I #11 Dec 23 2014 16:11:16
%S 0,0,840,12477384,2545607472,116307115440,2406303387000,
%T 30037635498360,262918567435104,1765904422135392,9653659287290280,
%U 44745048366882600,181129909217550480,654743996230865424,2149893215016113112,6499426966335074520,18286786291862020800
%N Number of ways of n-coloring the square grid graph G_(4,4) such that no rectangle exists with sides parallel to the axes having all 4 corners of the same color.
%C The square grid graph G_(4,4) has 16 vertices, 24 edges and 36 rectangles with sides parallel to the axes.
%C a(4) = A200045(4,4) = 2545607472.
%H Alois P. Heinz, <a href="/A252780/b252780.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) *(n^14 +n^13 +n^12 -35*n^11 -35*n^10 +61*n^9 +547*n^8 -101*n^7 -1797*n^6 -633*n^5 +5655*n^4 -5625*n^3 +3684*n^2 -2436*n +852).
%F G.f.: -24 *x^2 *(1473*x^14 +32720*x^13 +4197221*x^12 +209614896*x^11 +3974036005*x^10 +33181507744*x^9 +132190513545*x^8 +263917493088*x^7 +267855509283*x^6 +135288479760*x^5 +31950100783*x^4 +3113672560*x^3 +97233591*x^2 +519296*x+35) / (x-1)^17.
%p a:= n-> ((((((((((((n^3-36)*n^2+96)*n+486)*n-648)*n-1696)*n
%p +1164)*n+6288)*n-11280)*n+9309)*n-6120)*n+3288)*n-852)*n:
%p seq(a(n), n=0..30);
%Y Cf. A200045, A252778, A252779, A252839.
%K nonn,easy
%O 0,3
%A _Alois P. Heinz_, Dec 21 2014
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