A223249 Two-loop graph coloring a rectangular array: number of n X 2 0..4 arrays where 0..4 label nodes of a graph with edges 0,1 1,2 2,0 0,3 3,4 4,0 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

12, 52, 236, 1076, 4908, 22388, 102124, 465844, 2124972, 9693172, 44215916, 201693236, 920034348, 4196785268, 19143857644, 87325717684, 398340873132, 1817052930292, 8288582905196, 37808808665396, 172466877516588

Offset

1,1

Comments

Column 2 of A223255.

Links

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

Formula

Empirical: a(n) = 5*a(n-1) - 2*a(n-2).

Conjectures from Colin Barker, Mar 16 2018: (Start)

G.f.: 4*x*(3 - 2*x) / (1 - 5*x + 2*x^2).

a(n) = (2^(1-n)*((5-sqrt(17))^n*(-1+sqrt(17)) + (1+sqrt(17))*(5+sqrt(17))^n)) / sqrt(17).

(End)

Example

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

Crossrefs

Cf. A223255.

Sequence in context: A185355 A339029 A297757 * A195544 A248135 A307916

Adjacent sequences: A223246 A223247 A223248 * A223250 A223251 A223252

Keyword

nonn

Author

R. H. Hardin, Mar 18 2013

Status

approved