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A205633 Expansion of f(x^3, x^7) in powers of x where f() is Ramanujan's two-variable theta function. 2
1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 1, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

M. Somos, Introduction to Ramanujan theta functions

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

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Euler transform of period 20 sequence [ 0, 0, 1, 0, 0, -1, 1, 0, 0, -1, 0, 0, 1, -1, 0, 0, 1, 0, 0, -1, ...]. - Michael Somos, Sep 22 2012

Characteristic function of A036666: a(n) = 1 if and only if n is in A036666.

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

a(3*n + 2) = a(4*n + 1) = a(4*n + 2) = 0. a(4*n + 3) = A205988(n). - Michael Somos, Sep 22 2012

EXAMPLE

1 + x^3 + x^7 + x^16 + x^24 + x^39 + x^51 + x^72 + x^88 + x^115 + x^135 + ...

q + q^16 + q^36 + q^81 + q^121 + q^196 + q^256 + q^361 + q^441 + q^576 + ...

MATHEMATICA

A205633[n_] := SeriesCoefficient[QPochhammer[-q^3, q^10]* QPochhammer[-q^7, q^10]*QPochhammer[q^10, q^10], {q, 0, n}]; Table[A205633[n], {n, 0, 50}] (* G. C. Greubel, Jun 16 2017 *)

PROG

(PARI) {a(n) = issquare(5*n + 1)} /* Michael Somos, Sep 22 2012 */

CROSSREFS

Cf. A036666, A205988.

Sequence in context: A304362 A330682 A230135 * A252488 A170956 A293449

Adjacent sequences:  A205630 A205631 A205632 * A205634 A205635 A205636

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Feb 02 2012

STATUS

approved

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Last modified January 29 01:54 EST 2020. Contains 331328 sequences. (Running on oeis4.)