A223337 5 X 5 X 5 triangular graph coloring a rectangular array: number of n X 1 0..14 arrays where 0..14 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 3,6 3,7 4,7 6,7 4,8 5,8 7,8 5,9 8,9 6,10 6,11 7,11 10,11 7,12 8,12 11,12 11,12 8,13 9,13 12,13 9,14 13,14 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

15, 60, 264, 1176, 5280, 23712, 106560, 478848, 2151936, 9670656, 43459584, 195305472, 877694976, 3944325120, 17725636608, 79658287104, 357981093888, 1608752431104, 7229667803136, 32489832185856, 146007980507136

Offset

1,1

Comments

Column 1 of A223344.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) + 4*a(n-2) - 8*a(n-3).

Empirical g.f.: 3*x*(5 - 12*x^2) / (1 - 4*x - 4*x^2 + 8*x^3). - Colin Barker, Aug 19 2018

Example

Some solutions for n=3:
..3...11...11....9....4...11....4....5...10....6....8....7....2....8....4....8
..7....7...10....8....7....7....5....8....6....7....4....4....4....9....2...12
..3....8....6....7....3....6....8...12....3....6....7....7....7....5....5...11

Crossrefs

Cf. A223344.

Sequence in context: A206238 A064761 A005945 * A110755 A206231 A001756

Adjacent sequences: A223334 A223335 A223336 * A223338 A223339 A223340

Keyword

nonn

Author

R. H. Hardin, Mar 19 2013

Status

approved