%I #4 Mar 21 2013 04:41:31

%S 81,3539,182901,9685063,515473927,27465794119,1463848507173,

%T 78024299447333,4158831849750231,221674060909378867,

%U 11815685765605683663,629800688938588467995,33569692923595929936491,1789334831509984492336661

%N Petersen graph (3,1) coloring a rectangular array: number of nX5 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,3 3,5 3,4 1,2 1,4 4,5 2,0 2,5 and every array movement to a horizontal, diagonal or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0

%C Column 5 of A223504

%H R. H. Hardin, <a href="/A223501/b223501.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 80*a(n-1) -1601*a(n-2) +9025*a(n-3) +32750*a(n-4) -458870*a(n-5) +1007560*a(n-6) +2753424*a(n-7) -13680802*a(n-8) +9570798*a(n-9) +33912359*a(n-10) -66671806*a(n-11) +25819908*a(n-12) +31393403*a(n-13) -30099964*a(n-14) +2740719*a(n-15) +5650986*a(n-16) -2070082*a(n-17) -348*a(n-18) +116444*a(n-19) -20740*a(n-20) +1120*a(n-21)

%e Some solutions for n=3

%e ..0..2..0..2..0....0..3..5..3..5....0..3..4..5..3....0..3..0..3..4

%e ..0..2..5..2..5....0..3..5..2..0....0..1..4..5..3....0..3..0..1..4

%e ..5..2..1..2..5....5..2..0..2..1....4..1..2..5..3....4..3..0..1..2

%K nonn

%O 1,1

%A _R. H. Hardin_ Mar 21 2013