A245868 Number of length n+2 0..7 arrays with some pair in every consecutive three terms totalling exactly 7.

168, 712, 2368, 8840, 31176, 113024, 404264, 1455496, 5223552, 18775816, 67437448, 242306240, 870461352, 3127322696, 11235107264, 40363689352, 145010699592, 520968428032, 1871637364264, 6724074597128, 24157004951808, 86786820122120

Offset

1,1

Links

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

Robert Israel, Maple-assisted derivation of recurrence

Formula

Empirical: a(n) = 2*a(n-1) + 6*a(n-2) - a(n-3).

Empirical g.f.: 8*x*(21 + 47*x - 8*x^2) / (1 - 2*x - 6*x^2 + x^3). - Colin Barker, Nov 04 2018

Empirical recurrence verified: see link. - Robert Israel, May 13 2020

Example

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

Crossrefs

Column 7 of A245869.

Sequence in context: A157998 A234823 A234816 * A251461 A110285 A302887

Adjacent sequences: A245865 A245866 A245867 * A245869 A245870 A245871

Keyword

nonn

Author

R. H. Hardin, Aug 04 2014

Status

approved