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A089798 Expansion of Jacobi theta function theta_4(q^2). 2
1, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 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, -2, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000

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.

FORMULA

For n > 0, a(n) = 2*(floor(sqrt(n/2)) - floor(sqrt((n-1)/2)))*(-1)^floor(sqrt(n/2)). - Mikael Aaltonen, Jan 18 2015

MATHEMATICA

a[n_] := SeriesCoefficient[ EllipticTheta[4, 0, q^2], {q, 0, n}]; Table[a[n], {n, 0, 101}] (* Jean-Fran├žois Alcover, Nov 12 2012 *)

PROG

(PARI) for(n=0, 50, print1(if(n==0, 1, 2*(floor(sqrt(n/2)) - floor(sqrt((n-1)/2)))*(-1)^floor(sqrt(n/2))), ", ")) \\ G. C. Greubel, Nov 20 2017

CROSSREFS

Cf. A002448.

Sequence in context: A316897 A151756 A112053 * A070536 A318886 A030201

Adjacent sequences:  A089795 A089796 A089797 * A089799 A089800 A089801

KEYWORD

sign

AUTHOR

Eric W. Weisstein, Nov 12 2003

STATUS

approved

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Last modified April 13 16:27 EDT 2021. Contains 342936 sequences. (Running on oeis4.)