A201813 Number of arrays of 5 integers in -n..n with sum zero and equal numbers of elements greater than zero and less than zero.

51, 221, 631, 1401, 2651, 4501, 7071, 10481, 14851, 20301, 26951, 34921, 44331, 55301, 67951, 82401, 98771, 117181, 137751, 160601, 185851, 213621, 244031, 277201, 313251, 352301, 394471, 439881, 488651, 540901, 596751, 656321, 719731

Offset

1,1

Comments

Row 5 of A201811.

Links

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

Formula

Empirical: a(n) = 20*n^3 + 30*n + 1.

Conjectures from Colin Barker, May 25 2018: (Start)

G.f.: x*(51 + 17*x + 53*x^2 - x^3) / (1 - x)^4.

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

(End)

Example

Some solutions for n=17.
..6...13...-8...15..-12...-6...15....0..-13...-5...16....0...17...-4...-3...11
..0...-2....9....3...-2....0..-12....3....0..-17..-17..-16....5....0....0...-8
.-8..-12....7...-8....0....6...13...13..-11...12....0...-7...-5...13....7....0
..6....0...-8..-10....1...-3..-16..-10....8...10....3....8..-17..-16....1....2
.-4....1....0....0...13....3....0...-6...16....0...-2...15....0....7...-5...-5

Crossrefs

Cf. A201811.

Sequence in context: A158640 A107253 A030535 * A193250 A204717 A253921

Adjacent sequences: A201810 A201811 A201812 * A201814 A201815 A201816

Keyword

nonn

Author

R. H. Hardin, Dec 05 2011

Status

approved