A223425 5 X 5 X 5 triangular graph without horizontal edges 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 1,3 1,4 2,4 2,5 3,6 3,7 4,7 4,8 5,8 5,9 6,10 6,11 7,11 7,12 8,12 8,13 9,13 9,14 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

15, 40, 120, 356, 1088, 3276, 10052, 30380, 93296, 282240, 866908, 2623264, 8057756, 24384556, 74901596, 226673608, 696270792, 2107127204, 6472442928, 19587617308, 60167110388, 182084416108, 559307110768, 1692637810416, 5199260845212

Offset

1,1

Comments

Column 1 of A223432.

Links

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

Formula

Empirical: a(n) = 14*a(n-2) - 49*a(n-4) + 49*a(n-6) for n>7.

Empirical g.f.: x*(15 + 40*x - 90*x^2 - 204*x^3 + 143*x^4 + 252*x^5 - 35*x^6) / ((1 - 7*x^2 + 7*x^3)*(1 - 7*x^2 - 7*x^3)). - Colin Barker, Aug 20 2018

Example

Some solutions for n=3:
..5....1....8....3....2....2...10....6....4....7....2....7....0....2....4....8
..8....4....5....7....5....4....6....3....8....3....0....3....2....4....2....5
.13....2....8...12....2....2....3....6....5....1....2....7....4....8....4....9

Crossrefs

Cf. A223432.

Sequence in context: A067724 A005337 A160891 * A175926 A038991 A068020

Adjacent sequences: A223422 A223423 A223424 * A223426 A223427 A223428

Keyword

nonn

Author

R. H. Hardin, Mar 20 2013

Status

approved