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A223554 Petersen graph (3,1) coloring a rectangular array: number of nX6 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 A223554 #6 Jun 02 2025 08:29:27
%S A223554 243,44217,8410671,1609602003,308267930115,59043582882099,
%T A223554 11308909481307639,2166053304537606339,414875312906229086427,
%U A223554 79463200007529976606227,15219994937262513427990431
%N A223554 Petersen graph (3,1) coloring a rectangular array: number of nX6 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 A223554 Column 6 of A223556
%H A223554 R. H. Hardin, <a href="/A223554/b223554.txt">Table of n, a(n) for n = 1..210</a>
%F A223554 Empirical: a(n) = 229*a(n-1) -7630*a(n-2) +89386*a(n-3) -465129*a(n-4) +1124537*a(n-5) -1178896*a(n-6) +505856*a(n-7) -65536*a(n-8) for n>9
%e A223554 Some solutions for n=3
%e A223554 ..0..1..0..3..0..1....0..1..0..1..0..3....0..1..0..1..4..5....0..1..0..1..4..5
%e A223554 ..0..1..0..1..4..1....0..1..0..3..0..3....0..1..2..5..4..1....0..1..2..5..2..5
%e A223554 ..0..1..2..1..2..5....4..3..0..3..0..2....2..5..4..5..4..3....2..5..2..5..3..5
%K A223554 nonn
%O A223554 1,1
%A A223554 _R. H. Hardin_ Mar 22 2013