%I #11 Feb 16 2025 08:33:24
%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="https://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,changed
%O 0,3
%A _Alois P. Heinz_, Dec 21 2014