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
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
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
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 *)
PROG
(PARI) {a(n) = polcoeff((sum(k=0, 12, x^k))^n, 6*n, x)} \\ Seiichi Manyama, Dec 14 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, Dec 02 2011
EXTENSIONS
a(0)=1 prepended by Seiichi Manyama, Dec 14 2018
STATUS
approved