login
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
OFFSET
1,1
COMMENTS
Column 2 of A223255.
LINKS
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 18 2013
STATUS
approved