A143240 Expansion of Product_{k>0} (1 - x^(3*k)) / (1 - x^(3*k - 1)).

1, 0, 1, -1, 1, 0, 0, 0, 0, 0, 1, -1, 1, -1, 0, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 1, -1, 1, 0, -1, 1, -1, 0, 1, -1, 1, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, -1, 1, 0, 0, 1, -1, 0, 1, -1, 0, 0, -1, 1, 1, -1, 1, -1, 0, 1, 0, -1, 1, -1, 0, 1, -1, 0, 1, -1, 1, 0, -1, 1, 0, -1, 1, 0, 0, 0, 0, -1, 1, 0, -1, 1, -1, 0, 2, -1, 0, 1, -1

Offset

0,101

Comments

|a(n)|<2 if n<100, |a(n)|<3 if n<175.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Formula

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

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

Example

1 + q^2 - q^3 + q^4 + q^10 - q^11 + q^12 - q^13 + q^15 - q^19 + q^20 + ...

Prog

(PARI) {a(n) = if( n<0, 0, polcoeff( prod(k=1, (n+1)\3, (1 - x^(3*k)) / (1 - x^(3*k - 1)), 1 + x * O(x^n)), n))}

Crossrefs

Cf. A113706.

Sequence in context: A092147 A208134 A175560 * A363338 A290260 A304273

Adjacent sequences: A143237 A143238 A143239 * A143241 A143242 A143243

Keyword

sign

Author

Michael Somos, Aug 01 2008

Status

approved