A201550 Number of arrays of n integers in -6..6 with sum zero.

1, 1, 13, 127, 1469, 17151, 204763, 2473325, 30162301, 370487485, 4577127763, 56813989827, 707972099627, 8851373201919, 110976634957761, 1394804756117877, 17567994350713469, 221690794842728445, 2802194053806820153

Offset

0,3

Comments

Also largest coefficient of (1+x+...+x^12)^n. - Vaclav Kotesovec, Aug 09 2013

Links

Seiichi Manyama, Table of n, a(n) for n = 0..450 (terms 1..210 from R. H. Hardin) [It was suggested that the initial terms of this b-file were wrong, but in fact they are correct. - N. J. A. Sloane, Jan 19 2019]

Vaclav Kotesovec, Recurrence

Formula

a(n) ~ 13^n / sqrt(28*Pi*n). - Vaclav Kotesovec, Aug 09 2013

Example

Some solutions for n=5
.-2...-5...-2...-1....3...-6....0...-3....1....6...-6...-2....5....0...-4...-3
..2...-3...-2....3....0...-1....6...-4....6....1....5....2...-1....3....2....3
..0...-4....4...-6...-4....1...-3....0...-4...-5....0...-6...-3....0....4...-4
..0....6....3....5...-5....6....0....4....3...-4....4....0...-5...-3....3...-1
..0....6...-3...-1....6....0...-3....3...-6....2...-3....6....4....0...-5....5

Mathematica

Table[Coefficient[Expand[Sum[x^j, {j, 0, 12}]^n], x^(6*n)], {n, 1, 20}] (* Vaclav Kotesovec, Aug 09 2013 *)

Prog

(PARI) {a(n) = polcoeff((sum(k=0, 12, x^k))^n, 6*n, x)} \\ Seiichi Manyama, Dec 14 2018

Crossrefs

Column 6 of A201552.

Cf. A001405, A002426, A005190, A005191, A018901, A025012, A025013, A025014, A025015, A201549, A225779.

Sequence in context: A089763 A124298 A201040 * A361068 A211897 A147669

Adjacent sequences: A201547 A201548 A201549 * A201551 A201552 A201553

Keyword

nonn

Author

R. H. Hardin, Dec 02 2011

Extensions

a(0)=1 prepended by Seiichi Manyama, Dec 14 2018

Status

approved