%I #8 Aug 21 2018 05:54:43

%S 6,19,115,631,3539,19759,110427,617015,3447747,19265087,107648363,

%T 601511175,3361088979,18780896143,104942791931,586393188311,

%U 3276613524707,18308869209055,102305227390859,571655159691687

%N 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, diagonal or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0.

%C Row 2 of A223504.

%H R. H. Hardin, <a href="/A223505/b223505.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) + 4*a(n-2) - 4*a(n-3) for n>4.

%F Empirical g.f.: x*(2 - x)*(1 - 2*x)*(3 + 2*x) / (1 - 5*x - 4*x^2 + 4*x^3). - _Colin Barker_, Aug 21 2018

%e Some solutions for n=3:

%e ..0..1..0....0..3..0....0..2..0....0..2..1....0..2..1....0..1..4....0..1..0

%e ..0..1..4....5..3..5....5..2..5....1..2..0....0..2..0....4..1..0....2..1..0

%Y Cf. A223504.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 21 2013