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A223552 Petersen graph (3,1) coloring a rectangular array: number of n X 4 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 A223552 #8 Aug 21 2018 05:54:54
%S A223552 27,1089,44217,1795473,72906921,2960456193,120212193177,4881332621169,
%T A223552 198211242377097,8048559615522273,326819564358379641,
%U A223552 13270825184845208913,538874719548919491177,21881530298548175795649
%N A223552 Petersen graph (3,1) coloring a rectangular array: number of n X 4 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 A223552 Column 4 of A223556.
%H A223552 R. H. Hardin, <a href="/A223552/b223552.txt">Table of n, a(n) for n = 1..210</a>
%F A223552 Empirical: a(n) = 41*a(n-1) - 16*a(n-2).
%F A223552 Conjectures from _Colin Barker_, Aug 21 2018: (Start)
%F A223552 G.f.: 9*x*(3 - 2*x) / (1 - 41*x + 16*x^2).
%F A223552 a(n) = 3*sqrt(3/11)*2^(-4-n)*((41-7*sqrt(33))^n*(-1+sqrt(33)) + (1+sqrt(33))*(41+7*sqrt(33))^n).
%F A223552 (End)
%e A223552 Some solutions for n=3:
%e A223552 ..0..2..0..2....0..1..2..5....0..2..0..2....0..2..1..4....0..1..0..1
%e A223552 ..0..1..0..2....2..1..4..5....1..2..0..2....5..4..5..2....2..1..2..1
%e A223552 ..4..1..0..2....4..3..4..5....5..3..5..4....5..2..1..0....4..1..4..3
%Y A223552 Cf. A223556.
%K A223552 nonn
%O A223552 1,1
%A A223552 _R. H. Hardin_, Mar 22 2013