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

Author

R. H. Hardin, Aug 04 2014

Keywords

• nonn

Examples

			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
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210
• Robert Israel, Maple-assisted derivation of recurrence

Crossrefs

Column 7 of A245869.

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