A203293 Number of arrays of 6 nondecreasing integers in -n..n with sum zero and equal numbers greater than zero and less than zero.

4, 10, 28, 69, 154, 310, 580, 1013, 1680, 2662, 4064, 6005, 8634, 12114, 16644, 22441, 29760, 38878, 50116, 63817, 80374, 100206, 123784, 151609, 184240, 222266, 266340, 317149, 375446, 442022, 517740, 603501, 700284, 809110, 931080, 1067341, 1219126

Offset

1,1

Comments

Row 3 of A203291.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) -a(n-2) -4*a(n-3) +2*a(n-4) +2*a(n-5) +2*a(n-6) -4*a(n-7) -a(n-8) +3*a(n-9) -a(n-10).

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

Example

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

Crossrefs

Cf. A203291.

Sequence in context: A034920 A274597 A335548 * A111308 A348057 A121302

Adjacent sequences: A203290 A203291 A203292 * A203294 A203295 A203296

Keyword

nonn

Author

R. H. Hardin, Dec 31 2011

Status

approved