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
Keywords
Examples
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
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Crossrefs
Cf. A223255.
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)
Comments