A133101 Expansion of f(x^2, x^3) in powers of x where f(, ) is Ramanujan's general theta function.

1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

0,1

Links

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

Index entries for characteristic functions

Formula

The characteristic function of A057569.

Euler transform of period 10 sequence [ 0, 1, 1, -1, -1, -1, 1, 1, 0, -1, ...].

G.f.: Prod_{k>0} (1 - x^(5*k)) * (1 + x^(5*k - 2)) * (1 + x^(5*k - 3)) = Sum_{k in Z} x^((5*k^2 + k) / 2).

a(n) = abs(A113428(n)).

Example

G.f. = 1 + x^2 + x^3 + x^9 + x^11 + x^21 + x^24 + x^38 + x^42 + x^60 + x^65 + ...
G.f. = q + q^81 + q^121 + q^361 + q^441 + q^841 + q^961 + q^1521 + q^1681 + ...

Mathematica

a[ n_] := SeriesCoefficient[ QPochhammer[ -x^2, x^5] QPochhammer[ -x^3, x^5] QPochhammer[ x^5], {x, 0, n}]; (* Michael Somos, Oct 31 2015 *)

Prog

(PARI) {a(n) = if( n<0, 0, polcoeff( prod(k=1, n, 1 + x^k*[ -1, 0, 1, 1, 0][k%5 + 1], 1 + x * O(x^n)), n))};

Crossrefs

Cf. A057569, A113428.

Sequence in context: A267878 A231367 A113428 * A258769 A266377 A266326

Adjacent sequences: A133098 A133099 A133100 * A133102 A133103 A133104

Keyword

nonn

Author

Michael Somos, Sep 11 2007

Status

approved