A221685 Number of 0..n arrays of length 6 with each element differing from at least one neighbor by 1 or less, starting with 0.

32, 113, 241, 418, 636, 891, 1182, 1509, 1872, 2271, 2706, 3177, 3684, 4227, 4806, 5421, 6072, 6759, 7482, 8241, 9036, 9867, 10734, 11637, 12576, 13551, 14562, 15609, 16692, 17811, 18966, 20157, 21384, 22647, 23946, 25281, 26652, 28059, 29502, 30981

Offset

1,1

Comments

Row 6 of A221683.

Links

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

Formula

Empirical: a(n) = 18*n^2 + 57*n - 99 for n>4.

Conjectures from Colin Barker, Aug 10 2018: (Start)

G.f.: x*(32 + 17*x - 2*x^2 + 2*x^3 - 8*x^4 - 4*x^5 - x^6) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>7.

(End)

Example

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

Crossrefs

Cf. A221683.

Sequence in context: A203728 A044283 A044664 * A203721 A231527 A298201

Adjacent sequences: A221682 A221683 A221684 * A221686 A221687 A221688

Keyword

nonn

Author

R. H. Hardin, Jan 22 2013

Status

approved