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

1,1

Comments

Column 1 of A223218.

Links

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

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)

Example

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

Crossrefs

Cf. A223218.

Sequence in context: A227809 A119106 A223468 * A334330 A144706 A074427

Adjacent sequences: A223208 A223209 A223210 * A223212 A223213 A223214

Keyword

nonn

Author

R. H. Hardin, Mar 18 2013

Status

approved