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

1,1

Comments

Column 3 of A223504.

Links

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

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)

Example

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

Crossrefs

Cf. A223504.

Sequence in context: A379522 A157551 A157570 * A380973 A362774 A157233

Adjacent sequences: A223496 A223497 A223498 * A223500 A223501 A223502

Keyword

nonn

Author

R. H. Hardin, Mar 21 2013

Status

approved