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

Author

R. H. Hardin, Dec 02 2011

Keywords

• nonn
• easy

Comments

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

Examples

			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
		

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
• Index entries for sequences of k-nomial coefficients

Crossrefs

Column 6 of A201552. Row 13 of A077042.

Programs

Maple

seq(add((-1)^k * binomial(n, k)*binomial(7*n-13*k-1, n-1), k = 0..floor(n/2)), n = 0..20); # Peter Bala, Oct 16 2024

Mathematica

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

PARI

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

Formula

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

a(n) = Sum_{k = 0..floor(n/2)} (-1)^k * binomial(n, k)*binomial(7*n-13*k-1, n-1). - Peter Bala, Oct 16 2024

Extensions

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