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

Author

R. H. Hardin, Jan 22 2013

Keywords

• nonn

Comments

Row 6 of A221683.

Examples

			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
		

Links

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

Crossrefs

Cf. A221683.

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)