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

Author

Michael Somos, Sep 11 2007

Keywords

• nonn

Examples

			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 + ...
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• Index entries for characteristic functions

Crossrefs

Cf. A057569, A113428.

Programs

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 *)

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))};

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)).