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A223558 Petersen graph (3,1) coloring a rectangular array: number of 3 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 A223558 #7 Aug 21 2018 08:28:25
%S A223558 36,243,3249,44217,609309,8410671,116124291,1603350909,22137868197,
%T A223558 305663255847,4220371688499,58271764766661,804573346481541,
%U A223558 11108952552823119,153384184751908707,2117815160357837997
%N A223558 Petersen graph (3,1) coloring a rectangular array: number of 3 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 A223558 Row 3 of A223556.
%H A223558 R. H. Hardin, <a href="/A223558/b223558.txt">Table of n, a(n) for n = 1..210</a>
%F A223558 Empirical: a(n) = 17*a(n-1) - 47*a(n-2) + 41*a(n-3) - 10*a(n-4) for n>6.
%F A223558 Empirical g.f.: 9*x*(4 - 41*x + 90*x^2 - 119*x^3 + 80*x^4 - 18*x^5) / ((1 - x)*(1 - 16*x + 31*x^2 - 10*x^3)). - _Colin Barker_, Aug 21 2018
%e A223558 Some solutions for n=3:
%e A223558 ..0..2..0....0..3..0....0..1..4....0..3..4....0..3..5....0..1..2....0..1..0
%e A223558 ..5..2..5....5..2..1....2..5..3....0..3..4....5..4..3....2..5..4....4..3..5
%e A223558 ..5..3..5....5..4..3....4..5..2....0..3..4....3..0..3....2..1..4....0..3..4
%Y A223558 Cf. A223556.
%K A223558 nonn
%O A223558 1,1
%A A223558 _R. H. Hardin_, Mar 22 2013