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A223555 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.

%I A223555 #6 Jun 02 2025 08:29:44
%S A223555 729,281763,116124291,48435199821,20248676896077,8468395670690901,
%T A223555 3541866135681593043,1481382428937450207651,619587781032925818024165,
%U A223555 259142468285816914838504985,108386290103616110374877972691
%N A223555 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 A223555 Column 7 of A223556
%H A223555 R. H. Hardin, <a href="/A223555/b223555.txt">Table of n, a(n) for n = 1..210</a>
%F A223555 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 A223555 Some solutions for n=3
%e A223555 ..0..1..0..3..0..3..4....0..1..0..3..5..4..1....0..1..0..1..0..3..5
%e A223555 ..0..1..0..2..0..3..0....0..1..0..2..1..4..5....0..1..0..2..5..4..1
%e A223555 ..0..3..0..1..4..1..4....0..3..5..2..5..4..3....0..3..0..3..5..2..1
%K A223555 nonn
%O A223555 1,1
%A A223555 _R. H. Hardin_ Mar 22 2013