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

Author

R. H. Hardin, Dec 31 2011

Keywords

• nonn

Comments

Row 2 of A203291.

Examples

			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
		

Links

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

Crossrefs

Cf. A203291.

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)