A111376 Let qf(a,q) = Product(1-a*q^j,j=0..infinity); g.f. is qf(q^3,q^7)*qf(q^5,q^7)*qf(q^6,q^7)/(qf(q,q^7)*qf(q^2,q^7)*qf(q^4,q^7)).

1, 1, 2, 1, 3, 1, 2, -1, 3, 1, 3, 1, 4, 2, -1, -1, 1, 3, 1, 4, 6, 1, -1, -4, 5, -3, 6, 4, 9, -4, -5, 0, -3, 4, 4, 18, 1, -3, -4, -7, 0, -3, 25, 1, 5, -11, -4, -12, -7, 32, 11, 15, -15, 4, -24, -21, 27, 21, 31, -24, 17, -41, -31, 4, 38, 50, -18, 36, -46, -41, -36, 45, 67, -12, 57, -50, -38, -95, 51, 73, 14, 82, -32, -27, -171, 44

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

Euler transform of period 7 sequence [1, 1, -1, 1, -1, -1, 0, ...]. - Michael Somos, Nov 11 2005

G.f.: Product_{k>0} (1-x^(7k-4))(1-x^(7k-2))(1-x^(7k-1))/((1-x^(7k-3))*(1-x^(7k-5))(1-x^(7k-6))). - Michael Somos, Nov 11 2005

Prog

(PARI) {a(n)=if(n<0, 0, polcoeff( prod(k=1, n, (1-x^k)^-kronecker(-7, k), 1+x*O(x^n)), n))} /* Michael Somos, Nov 11 2005 */

Crossrefs

Cf. A111375.

Sequence in context: A364447 A309978 A108103 * A241664 A157226 A156249

Adjacent sequences: A111373 A111374 A111375 * A111377 A111378 A111379

Keyword

sign,look

Author

N. J. A. Sloane, Nov 09 2005

Status

approved