A205988 Expansion of f(x^1, x^9) in powers of x where f(, ) is Ramanujan's general theta function.

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

Offset

0

Comments

Characteristic function of A195162. - Jason Kimberley, Nov 15 2012

Links

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

S. Cooper and M. D. Hirschhorn, Results of Hurwitz type for three squares. Discrete Math. 274 (2004), no. 1-3, 9-24. See E(q).

Michael Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

Formula

G.f.: f(x, x^9) = Sum_{k in Z} x^(5*k^2 + 4*k).

Example

G.f. = 1 + x + x^9 + x^12 + x^28 + x^33 + x^57 + x^64 + x^96 + x^105 + x^145 + ...

Mathematica

CoefficientList[Series[QPochhammer[-q, q^10]* QPochhammer[-q^9, q^10]*QPochhammer[q^10, q^10], {q, 0, 160}], q] (* G. C. Greubel, Aug 12 2018 *)

Crossrefs

Sequence in context: A016373 A281815 A353633 * A167700 A010057 A359548

Adjacent sequences: A205985 A205986 A205987 * A205989 A205990 A205991

Keyword

nonn,easy

Author

N. J. A. Sloane, Feb 02 2012

Status

approved