A203287 Number of arrays of 2n nondecreasing integers in -4..4 with sum zero and equal numbers greater than zero and less than zero.

5, 21, 69, 188, 444, 944, 1844, 3369, 5825, 9621, 15285, 23492, 35080, 51084, 72756, 101601, 139401, 188257, 250613, 329304, 427584, 549176, 698304, 879749, 1098881, 1361721, 1674977, 2046108, 2483364, 2995856, 3593596, 4287573, 5089797, 6013377

Offset: 1

Author

R. H. Hardin, Dec 31 2011

Keywords

• nonn

Comments

Column 4 of A203291.

Examples

			Some solutions for n=3:
.-3...-1...-3...-3...-3...-3...-3...-4...-3...-4...-4...-3...-2...-4...-4...-4
.-3...-1...-2...-3...-2...-3...-3...-1...-2....0...-2...-1....0...-2...-2...-4
.-1...-1....0...-2...-1...-1...-1...-1....0....0...-1...-1....0...-2...-1...-1
..1....1....0....1....1....1....2....1....0....0....1....1....0....2....2....3
..3....1....2....3....1....2....2....2....1....0....2....2....0....3....2....3
..3....1....3....4....4....4....3....3....4....4....4....2....2....3....3....3
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..189

Crossrefs

Cf. A203291.

Formula

Empirical: a(n) = 4*a(n-1) -4*a(n-2) -3*a(n-3) +6*a(n-4) -6*a(n-7) +3*a(n-8) +4*a(n-9) -4*a(n-10) +a(n-11).

Empirical g.f.: x*(5 + x + 5*x^2 + 11*x^3 + x^4 + x^5 - 6*x^6 + 3*x^7 + 4*x^8 - 4*x^9 + x^10) / ((1 - x)^7*(1 + x)^2*(1 + x + x^2)). - Colin Barker, Jun 04 2018