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, 31893473567409732813, 465851764737061437765
Offset: 0
Keywords
Examples
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
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]
Crossrefs
Column 7 of A201552.
Programs
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Maple
seq(add((-1)^k*binomial(n, k)*binomial(8*n-15*k-1, n-1), k = 0..floor(n/2)), n = 0..20); # Peter Bala, Oct 19 2024
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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 *) -
PARI
{a(n) = polcoeff((sum(k=0, 14, x^k))^n, 7*n, x)} \\ Seiichi Manyama, Dec 14 2018
Formula
a(n) ~ sqrt(3) * 15^n / (4*sqrt(7*Pi*n)). - Vaclav Kotesovec, Dec 15 2018
Extensions
a(0)=1 prepended by Seiichi Manyama, Dec 14 2018