A223687 Petersen graph (8,2) coloring a rectangular array: number of n X 3 0..15 arrays where 0..15 label nodes of a graph with edges 0,1 0,8 8,14 8,10 1,2 1,9 9,15 9,11 2,3 2,10 10,12 3,4 3,11 11,13 4,5 4,12 12,14 5,6 5,13 13,15 6,7 6,14 7,0 7,15 and every array movement to a horizontal or antidiagonal neighbor moves along an edge of this graph.

144, 2304, 37008, 595584, 9594000, 154616832, 2492365968, 40180445568, 647800215696, 10444288589568, 168392298756240, 2714990519274624, 43773950520548496, 705771016545286656, 11379212680977220752

Offset

1,1

Comments

Column 3 of A223692.

Links

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

Formula

Empirical: a(n) = 24*a(n-1) - 127*a(n-2).

Conjectures from Colin Barker, Aug 22 2018: (Start)

G.f.: 144*x*(1 - 8*x) / (1 - 24*x + 127*x^2).

a(n) = (72*((12-sqrt(17))^n*(-31+8*sqrt(17)) + (12+sqrt(17))^n*(31+8*sqrt(17)))) / (127*sqrt(17)).

(End)

Example

Some solutions for n=3:
.14..8.14...13..5..6...14..8.14...13.15..9....0..8.14....7.15..9....3.11.13
.10.12.14....6..5..6....0..8.10....9.15.13...14.12..4...13.15.13....3.11.13
.14..8..0....4..5..4...10..8.10...13.11..9....4..5.13...13.11..3...13.15..9

Crossrefs

Cf. A223692.

Sequence in context: A008431 A250084 A280025 * A268625 A121344 A232819

Adjacent sequences: A223684 A223685 A223686 * A223688 A223689 A223690

Keyword

nonn

Author

R. H. Hardin, Mar 25 2013

Status

approved