A221517 Number of 0..n arrays of length 6 with each element differing from at least one neighbor by 2 or more, starting with 0.

0, 5, 89, 532, 1970, 5513, 12872, 26477, 49598, 86465, 142388, 223877, 338762, 496313, 707360, 984413, 1341782, 1795697, 2364428, 3068405, 3930338, 4975337, 6231032, 7727693, 9498350, 11578913, 14008292, 16828517, 20084858, 23825945

Offset: 1

Author

R. H. Hardin, Jan 18 2013

Keywords

• nonn

Comments

Row 6 of A221515.

Examples

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

Links

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

Crossrefs

Cf. A221515.

Formula

Empirical: a(n) = 1*n^5 - 20*n^3 + 78*n^2 - 146*n + 125 for n>4.

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

G.f.: x^2*(5 + 59*x + 73*x^2 + 13*x^3 - 32*x^4 + 9*x^5 - 9*x^6 + 3*x^7 - x^8) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>10.

(End)