A223408 4 X 4 X 4 triangular graph without horizontal edges coloring a rectangular array: number of n X 1 0..9 arrays where 0..9 label nodes of a graph with edges 0,1 0,2 1,3 1,4 2,4 2,5 3,6 3,7 4,7 4,8 5,8 5,9 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

10, 24, 66, 176, 486, 1312, 3622, 9792, 27030, 73088, 201750, 545536, 1505878, 4071936, 11240022, 30393344, 83896662, 226859008, 626213206, 1693298688, 4674118998, 12638953472, 34888099158, 94338433024, 260408317270

Offset

1,1

Comments

Column 1 of A223415.

Links

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

Formula

Empirical: a(n) = 9*a(n-2) - 12*a(n-4) + 4*a(n-6).

Empirical g.f.: 2*x*(5 + 12*x - 12*x^2 - 20*x^3 + 6*x^4 + 8*x^5) / ((1 - x)*(1 + x)*(1 + 2*x - 2*x^2)*(1 - 2*x - 2*x^2)). - Colin Barker, Aug 20 2018

Example

Some solutions for n=3:
..1....7....4....4....8....2....5....4....1....2....4....4....3....4....1....6
..4....4....7....8....4....0....2....2....0....4....8....1....6....2....4....3
..1....8....3....5....7....1....4....0....1....8....4....0....3....5....2....1

Crossrefs

Cf. A223415.

Sequence in context: A250798 A250576 A126911 * A261807 A135285 A235940

Adjacent sequences: A223405 A223406 A223407 * A223409 A223410 A223411

Keyword

nonn

Author

R. H. Hardin, Mar 20 2013

Status

approved