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A205988 Expansion of f(x^1, x^9) in powers of x where f(, ) is Ramanujan's general theta function. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0
COMMENTS
Characteristic function of A195162. - Jason Kimberley, Nov 15 2012
LINKS
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).
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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Feb 02 2012
STATUS
approved

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Last modified February 23 14:24 EST 2024. Contains 370283 sequences. (Running on oeis4.)