A201551 Number of arrays of n integers in -7..7 with sum zero.

1, 1, 15, 169, 2255, 30381, 418503, 5832765, 82073295, 1163205475, 16581420835, 237481736823, 3414582082055, 49258226347903, 712601187601395, 10334165623697259, 150186639579545295, 2186774434431445455

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..400 (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]

Formula

a(n) ~ sqrt(3) * 15^n / (4*sqrt(7*Pi*n)). - Vaclav Kotesovec, Dec 15 2018

Example

Some solutions for n=5
.-6....6....2...-1...-4...-5...-2...-2....4...-6....2....7...-5...-5....3....5
.-2....0....7...-3....2....6...-3....7...-4...-2...-7...-3....6....2...-3...-7
..0...-6...-5...-2....6....5....5...-5...-6....5....5....1...-4....4....1...-4
..2...-2...-4....0...-7...-5....6...-7....6....6...-5....1....4....5...-3....7
..6....2....0....6....3...-1...-6....7....0...-3....5...-6...-1...-6....2...-1

Mathematica

a[n_] := If[n==0, 1, Coefficient[Expand[Sum[x^k, {k, 0, 14}]^n], x^(7n)]]; Array[a, 25, 0] (* Amiram Eldar, Dec 14 2018 *)

Prog

(PARI) {a(n) = polcoeff((sum(k=0, 14, x^k))^n, 7*n, x)} \\ Seiichi Manyama, Dec 14 2018

Crossrefs

Column 7 of A201552.

Sequence in context: A016279 A036734 A201041 * A339770 A240276 A206600

Adjacent sequences: A201548 A201549 A201550 * A201552 A201553 A201554

Keyword

nonn

Author

R. H. Hardin, Dec 02 2011

Extensions

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

Status

approved