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Petersen graph (3,1) coloring a rectangular array: number of nX7 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 or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0
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%I #4 Mar 22 2013 05:36:00

%S 729,281763,116124291,48435199821,20248676896077,8468395670690901,

%T 3541866135681593043,1481382428937450207651,619587781032925818024165,

%U 259142468285816914838504985,108386290103616110374877972691

%N Petersen graph (3,1) coloring a rectangular array: number of nX7 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 or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0

%C Column 7 of A223556

%H R. H. Hardin, <a href="/A223555/b223555.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 579*a(n-1) -77474*a(n-2) +4635156*a(n-3) -154699059*a(n-4) +3198735625*a(n-5) -43344055546*a(n-6) +396489063452*a(n-7) -2477765391092*a(n-8) +10544713088920*a(n-9) -29940917775104*a(n-10) +54099319050624*a(n-11) -56116354684928*a(n-12) +25386144890880*a(n-13) for n>15

%e Some solutions for n=3

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Mar 22 2013