A221527 Number of 0..n arrays of length 7 with each element differing from at least one neighbor by 2 or more.

0, 16, 768, 8544, 50400, 205080, 654864, 1763328, 4184064, 9005400, 17936160, 33537504, 59505888, 101012184, 165102000, 261162240, 401458944, 601751448, 881987904, 1267087200, 1787812320, 2481740184, 3394333008, 4580116224

Offset: 1

Author

R. H. Hardin, Jan 19 2013

Keywords

• nonn

Comments

Row 7 of A221524.

Examples

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

Links

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

Crossrefs

Cf. A221524.

Formula

Empirical: a(n) = 1*n^7 + 1*n^6 - 29*n^5 + 109*n^4 - 204*n^3 + 202*n^2 - 80*n for n>2.

Conjectures from Colin Barker, Aug 06 2018: (Start)

G.f.: 8*x^2*(2 + 80*x + 356*x^2 + 332*x^3 - 97*x^4 - 22*x^5 - 28*x^6 + 8*x^7 - x^8) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>10.

(End)