A223338 5 X 5 X 5 triangular graph coloring a rectangular array: number of n X 2 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.

60, 612, 6696, 74736, 840456, 9474840, 106904016, 1206530100, 13618313028, 153717108696, 1735104803220, 19585324103616, 221073319268820, 2495410941230244, 28167472321321608, 317946242671782120

Offset

1,1

Comments

Column 2 of A223344.

Links

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

Formula

Empirical: a(n) = 13*a(n-1) - 11*a(n-2) - 94*a(n-3) - 7*a(n-4) + 79*a(n-5) - 3*a(n-6).

Empirical g.f.: 12*x*(5 - 14*x - 50*x^2 + 5*x^3 + 41*x^4 - 2*x^5) / (1 - 13*x + 11*x^2 + 94*x^3 + 7*x^4 - 79*x^5 + 3*x^6). - Colin Barker, Aug 19 2018

Example

Some solutions for n=3:
..4..3....4..3...12.13....3..7...13.14....7..4....4..1....8..7....8..4....8..9
..3..6....8..7....8.12....7..3...14..9....8..7....5..4....5..4....4..5....4..5
..6..3....4..3....5..8....3..7....9..5....4..3....4..2....9..8....5..9....3..4

Crossrefs

Cf. A223344.

Sequence in context: A184191 A101384 A229750 * A081384 A283786 A099344

Adjacent sequences: A223335 A223336 A223337 * A223339 A223340 A223341

Keyword

nonn

Author

R. H. Hardin, Mar 19 2013

Status

approved