A143277 G.f.: Product_{k>0} (1 - x^(3*k))^2 / (1 - x^(3*k - 2)).

1, 1, 1, -1, 0, 0, -1, -2, -1, 1, -1, -2, 0, 0, -1, 0, 2, 1, -2, 0, 1, 1, 1, 2, 0, 1, 1, -1, -1, 2, 3, -1, 0, 2, -1, -1, 1, 1, -3, 0, 0, -1, 1, 2, 0, -3, -1, -2, -2, 1, 0, -1, 0, 0, -2, 0, 2, -2, -1, 0, -2, -2, 1, 1, -1, 2, 0, -2, 1, 2, -1, 0, 3, -2, -1, 2, -1, -3, 3, 2, -1, 3, 5, -1, -2, 1, 0, 0, 1, -1, 0, 2, 0, 0, 3, 1, -2, 0, 0, 0, 4, 2, -3, 1, 1

Offset

0,8

Links

Table of n, a(n) for n=0..104.

Formula

Euler transform of period 3 sequence [ 1, 0, -2, ...].

Example

1 + q + q^2 - q^3 - q^6 - 2*q^7 - q^8 + q^9 - q^10 - 2*q^11 - q^14 + ...

Prog

(PARI) {a(n) = if( n<0, 0, polcoeff( prod(k=1, n, (1 - x^k)^([2, -1, 0][k%3 + 1]), 1 + x * O(x^n)), n))}

Crossrefs

Sequence in context: A230453 A098876 A364891 * A292378 A320835 A276183

Adjacent sequences: A143274 A143275 A143276 * A143278 A143279 A143280

Keyword

sign

Author

Michael Somos, Aug 04 2008

Status

approved