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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. 2
12, 52, 236, 1076, 4908, 22388, 102124, 465844, 2124972, 9693172, 44215916, 201693236, 920034348, 4196785268, 19143857644, 87325717684, 398340873132, 1817052930292, 8288582905196, 37808808665396, 172466877516588 (list; graph; refs; listen; history; text; internal format)
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: A054410 A185355 A297757 * A195544 A248135 A307916

Adjacent sequences:  A223246 A223247 A223248 * A223250 A223251 A223252

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 18 2013

STATUS

approved

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Last modified July 17 08:42 EDT 2019. Contains 325098 sequences. (Running on oeis4.)