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

Author

R. H. Hardin, Dec 31 2011

Keywords

• nonn

Comments

Row 3 of A203291.

Examples

			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
		

Links

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

Crossrefs

Cf. A203291.

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