%I #4 Mar 19 2013 17:10:37
%S 544,37008,2812608,215773456,16589428016,1275808315376,98124582178928,
%T 7547020636487088,580464274863214064,44645287470831363696,
%U 3433808133436891915472,264104805258676364046000
%N 3X3 square grid graph coloring a rectangular array: number of nX5 0..8 arrays where 0..8 label nodes of the square grid graph and every array movement to a horizontal or vertical neighbor moves along an edge of this graph
%C Column 5 of A223379
%H R. H. Hardin, <a href="/A223376/b223376.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 6529*a(n-2) -3729898*a(n-4) +606147188*a(n-6) -37186782450*a(n-8) +998979380722*a(n-10) -12128079473561*a(n-12) +73825567196497*a(n-14) -244037398666282*a(n-16) +453145801165820*a(n-18) -474188974363940*a(n-20) +277662926324048*a(n-22) -88145495115904*a(n-24) +14048888263168*a(n-26) -876794757120*a(n-28) for n>29
%e Some solutions for n=3
%e ..0..1..0..3..0....0..1..4..1..0....0..3..6..7..4....0..3..4..7..8
%e ..1..0..1..4..1....1..4..3..4..1....1..4..7..4..7....1..4..7..4..5
%e ..4..3..4..1..4....4..5..4..5..4....4..7..6..3..4....2..5..4..7..4
%e Vertex neighbors:
%e 0 -> 1 3
%e 1 -> 0 2 4
%e 2 -> 1 5
%e 3 -> 0 4 6
%e 4 -> 3 1 5 7
%e 5 -> 4 2 8
%e 6 -> 3 7
%e 7 -> 6 4 8
%e 8 -> 7 5
%K nonn
%O 1,1
%A _R. H. Hardin_ Mar 19 2013