A199902 Number of -n..n arrays x(0..6) of 7 elements with zero sum, and adjacent elements not both strictly positive and not both strictly negative.

171, 1783, 8823, 30199, 82555, 193689, 406575, 783989, 1413739, 2414499, 3942247, 6197307, 9431995, 13958869, 20159583, 28494345, 39511979, 53860591, 72298839, 95707807, 125103483, 161649841, 206672527, 261673149, 328344171, 408584411

Offset: 1

Author

R. H. Hardin, Nov 11 2011

Keywords

• nonn

Comments

Row 7 of A199898.

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A199898.

Formula

Empirical: a(n) = (151/180)*n^6 + (163/15)*n^5 + (377/9)*n^4 + (395/6)*n^3 + (7429/180)*n^2 + (93/10)*n + 1.

Conjectures from Colin Barker, May 17 2018: (Start)

G.f.: x*(171 + 586*x - 67*x^2 - 104*x^3 + 25*x^4 - 8*x^5 + x^6) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)