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

1,1

Comments

Column 4 of A203291.

Links

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

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

Example

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

Crossrefs

Cf. A203291.

Sequence in context: A147246 A335982 A271282 * A296720 A099899 A269566

Adjacent sequences: A203284 A203285 A203286 * A203288 A203289 A203290

Keyword

nonn

Author

R. H. Hardin, Dec 31 2011

Status

approved