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A223557 Petersen graph (3,1) coloring a rectangular array: number of 2 X n 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 A223557 #8 Aug 21 2018 06:31:08
%S A223557 6,27,171,1089,6939,44217,281763,1795473,11441259,72906921,464583411,
%T A223557 2960456193,18864859707,120212193177,766025913411,4881332621169,
%U A223557 31105224694539,198211242377097,1263057797861523,8048559615522273
%N A223557 Petersen graph (3,1) coloring a rectangular array: number of 2 X n 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 A223557 Row 2 of A223556.
%H A223557 R. H. Hardin, <a href="/A223557/b223557.txt">Table of n, a(n) for n = 1..210</a>
%F A223557 Empirical: a(n) = 7*a(n-1) - 4*a(n-2) for n>3.
%F A223557 Empirical g.f.: 3*x*(2 - x)*(1 - 2*x) / (1 - 7*x + 4*x^2). - _Colin Barker_, Aug 21 2018
%e A223557 Some solutions for n=3:
%e A223557 ..0..1..0....0..3..4....0..1..0....0..1..0....0..1..0....0..2..1....0..3..0
%e A223557 ..0..2..5....4..5..2....0..3..0....0..2..1....0..1..0....1..2..1....4..1..4
%Y A223557 Cf. A223556.
%K A223557 nonn
%O A223557 1,1
%A A223557 _R. H. Hardin_, Mar 22 2013