A223211 3 X 3 X 3 triangular graph coloring a rectangular array: number of n X 1 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,2 1,2 1,3 1,4 2,4 3,4 2,5 4,5 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

6, 18, 60, 192, 624, 2016, 6528, 21120, 68352, 221184, 715776, 2316288, 7495680, 24256512, 78495744, 254017536, 822018048, 2660106240, 8608284672, 27856994304, 90147127296, 291722231808, 944032972800, 3054954872832, 9886041636864

Offset: 1

Author

R. H. Hardin, Mar 18 2013

Keywords

• nonn

Comments

Column 1 of A223218.

Examples

			Some solutions for n=3:
..4....4....0....2....1....4....2....3....2....2....0....5....1....3....4....5
..2....1....1....5....2....2....1....1....0....1....1....4....3....4....3....2
..0....4....4....2....0....4....2....0....2....0....0....2....1....1....1....1
		

Links

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

Crossrefs

Cf. A223218.

Formula

Empirical: a(n) = 2*a(n-1) + 4*a(n-2) = 6*A063782(n-1).

Conjectures from Colin Barker, Aug 17 2018: (Start)

G.f.: 6*x*(1 + x) / (1 - 2*x - 4*x^2).

a(n) = (3*((1-sqrt(5))^n*(-3+sqrt(5)) + (1+sqrt(5))^n*(3+sqrt(5)))) / (4*sqrt(5)).

(End)