A199836 Number of -n..n arrays x(0..6) of 7 elements with zero sum and no two neighbors summing to zero.

22, 1650, 20240, 118280, 462234, 1402934, 3579520, 8046928, 16426926, 31082698, 55316976, 93593720, 151783346, 237431502, 360051392, 531439648, 766015750, 1081184994, 1497725008, 2040195816, 2737373450, 3622707110, 4734799872

Offset: 1

Author

R. H. Hardin, Nov 11 2011

Keywords

• nonn

Comments

Row 5 of A199832.

Examples

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

Links

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

Crossrefs

Cf. A199832.

Formula

Empirical: a(n) = (5887/180)*n^6 - (1013/60)*n^5 + (245/36)*n^4 - (35/12)*n^3 + (157/45)*n^2 - (6/5)*n.

Conjectures from Colin Barker, May 16 2018: (Start)

G.f.: 2*x*(11 + 748*x + 4576*x^2 + 5240*x^3 + 1167*x^4 + 32*x^5) / (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)