A223499 Petersen graph (3,1) coloring a rectangular array: number of n X 3 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.

9, 115, 1519, 20115, 266419, 3528715, 46737819, 619042315, 8199214219, 108598575915, 1438387920619, 19051445129515, 252336352607019, 3342194485203115, 44267359266773419, 586321084882796715

Offset: 1

Author

R. H. Hardin, Mar 21 2013

Keywords

• nonn

Comments

Column 3 of A223504.

Examples

			Some solutions for n=3:
..0..1..4....0..3..4....0..1..4....0..2..5....0..1..4....0..3..4....0..3..0
..0..3..0....4..3..5....2..1..0....0..3..0....4..3..0....4..3..4....4..3..0
..5..2..5....5..3..4....4..1..4....0..1..0....0..3..4....5..3..4....5..3..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Crossrefs

Cf. A223504.

Formula

Empirical: a(n) = 15*a(n-1) - 24*a(n-2) + 10*a(n-3).

Conjectures from Colin Barker, Aug 21 2018: (Start)

G.f.: x*(9 - 20*x + 10*x^2) / ((1 - x)*(1 - 14*x + 10*x^2)).

a(n) = (13 + (13-2*sqrt(39))*(7-sqrt(39))^n + (7+sqrt(39))^n*(13+2*sqrt(39))) / 39.

(End)