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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

%I

%S 0,0,156,14298,228984,1821420,9676020,39328086,131914608,382726584,

%T 991134540,2342199090,5133181416,10561434468,20593784484,38341504110,

%U 68569332960,118371718896,198054533628,322265959434,511426049880,793510636380,1206251784276

%N 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.

%C The square grid graph G_(3,3) has 9 vertices, 12 edges and 9 rectangles with sides parallel to the axes.

%C a(4) = A200045(3,3) = 228984.

%H Alois P. Heinz, <a href="/A252778/b252778.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^7+n^6+n^5-8*n^4-8*n^3+4*n^2+22*n-14).

%F 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.

%p a:= n-> (((((n^3-9)*n^2+12)*n+18)*n-36)*n+14)*n:

%p seq(a(n), n=0..30);

%Y Cf. A200045, A252779, A252780, A252839.

%K nonn,easy

%O 0,3

%A _Alois P. Heinz_, Dec 21 2014

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Last modified September 24 10:18 EDT 2020. Contains 337317 sequences. (Running on oeis4.)