A203286 Number of arrays of 2n nondecreasing integers in -3..3 with sum zero and equal numbers greater than zero and less than zero.

4, 12, 28, 57, 104, 176, 280, 425, 620, 876, 1204, 1617, 2128, 2752, 3504, 4401, 5460, 6700, 8140, 9801, 11704, 13872, 16328, 19097, 22204, 25676, 29540, 33825, 38560, 43776, 49504, 55777, 62628, 70092, 78204, 87001, 96520, 106800, 117880, 129801

Offset

1,1

Comments

Column 3 of A203291.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) -5*a(n-2) +5*a(n-4) -4*a(n-5) +a(n-6).

Conjectures from Colin Barker, Jun 04 2018: (Start)

G.f.: x*(4 - 4*x + 5*x^3 - 4*x^4 + x^5) / ((1 - x)^5*(1 + x)).

a(n) = (48 + 80*n + 52*n^2 + 16*n^3 + 2*n^4)/48 for n even.

a(n) = (42 + 80*n + 52*n^2 + 16*n^3 + 2*n^4)/48 for n odd.

(End)

Example

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

Crossrefs

Cf. A203291.

Sequence in context: A102653 A102650 A011939 * A028346 A356728 A079089

Adjacent sequences: A203283 A203284 A203285 * A203287 A203288 A203289

Keyword

nonn

Author

R. H. Hardin, Dec 31 2011

Status

approved