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A089806 Expansion of Jacobi theta function (theta_3(q^(1/3))-theta_2(q^3))/2/q^(1/12). 7
1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 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, 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, 0, 0, 0, 1, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..10034

Eric Weisstein's World of Mathematics, Jacobi Theta Functions

I. J. Zucker, Further Relations Amongst Infinite Series and Products. II. The Evaluation of Three-Dimensional Lattice Sums, J. Phys. A: Math. Gen. 23, 117-132, 1990.

Index entries for characteristic functions

FORMULA

Euler transform of period 12 sequence [0, 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, -1, ...]. - Michael Somos, Apr 13 2005

a(n) = b(12n+1) where b(n) is multiplicative and b(3^e)=0^e, b(p^e)=(1+(-1)^e)/2 if p<>3. - Michael Somos, Jun 06 2005

Expansion of q^(-1/12)(eta(q^4)eta(q^6)^2)/(eta(q^2)eta(q^12)) in powers of q.

EXAMPLE

1 + q^2 + q^4 + q^10 + q^14 + q^24 + q^30 + q^44 + q^52 + ...

MATHEMATICA

nmax = 100; CoefficientList[Series[Product[(1+x^(2*k)) * (1-x^(6*k)) / (1+x^(6*k)), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jul 05 2016 *)

PROG

(PARI) a(n)=issquare(12*n+1) /* Michael Somos, Apr 13 2005 */

(PARI) lista(nn) = {q='q+O('q^nn); Vec(eta(q^4)*eta(q^6)^2/(eta(q^2)*eta(q^12)))} \\ Altug Alkan, Mar 22 2018

CROSSREFS

Cf. A080995(n)=a(2n).

Sequence in context: A014165 A014141 A014093 * A274719 A014069 A154388

Adjacent sequences:  A089803 A089804 A089805 * A089807 A089808 A089809

KEYWORD

nonn

AUTHOR

Eric W. Weisstein, Nov 12 2003

STATUS

approved

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Last modified May 28 15:33 EDT 2020. Contains 334684 sequences. (Running on oeis4.)