A203292 Number of arrays of 4 nondecreasing integers in -n..n with sum zero and equal numbers greater than zero and less than zero.

3, 6, 12, 21, 35, 54, 80, 113, 155, 206, 268, 341, 427, 526, 640, 769, 915, 1078, 1260, 1461, 1683, 1926, 2192, 2481, 2795, 3134, 3500, 3893, 4315, 4766, 5248, 5761, 6307, 6886, 7500, 8149, 8835, 9558, 10320, 11121, 11963, 12846, 13772, 14741, 15755

Offset

1,1

Comments

Row 2 of A203291.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) -2*a(n-2) -2*a(n-3) +3*a(n-4) -a(n-5).

Conjectures from Colin Barker, Jun 04 2018: (Start)

G.f.: x*(3 - 3*x + 3*x^3 - x^4) / ((1 - x)^4*(1 + x)).

a(n) = (24 + 32*n + 6*n^2 + 4*n^3)/24 for n even.

a(n) = (30 + 32*n + 6*n^2 + 4*n^3)/24 for n odd.

(End)

Example

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

Crossrefs

Cf. A203291.

Sequence in context: A084439 A034344 A260640 * A054578 A115855 A234248

Adjacent sequences: A203289 A203290 A203291 * A203293 A203294 A203295

Keyword

nonn

Author

R. H. Hardin, Dec 31 2011

Status

approved