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

1,1

Comments

Row 5 of A199832.

Links

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

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)

Example

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

Crossrefs

Cf. A199832.

Sequence in context: A243478 A245658 A277664 * A196705 A196854 A196948

Adjacent sequences: A199833 A199834 A199835 * A199837 A199838 A199839

Keyword

nonn

Author

R. H. Hardin, Nov 11 2011

Status

approved