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

1,2

Comments

Row 6 of A221515.

Links

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

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)

Example

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

Crossrefs

Cf. A221515.

Sequence in context: A176608 A277233 A167735 * A264247 A348578 A360064

Adjacent sequences: A221514 A221515 A221516 * A221518 A221519 A221520

Keyword

nonn

Author

R. H. Hardin, Jan 18 2013

Status

approved