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

1,1

Comments

Row 7 of A199898.

Links

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

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)

Example

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

Crossrefs

Cf. A199898.

Sequence in context: A036518 A187133 A185838 * A251223 A186868 A185611

Adjacent sequences: A199899 A199900 A199901 * A199903 A199904 A199905

Keyword

nonn

Author

R. H. Hardin, Nov 11 2011

Status

approved