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%I #16 Nov 20 2017 23:30:41
%S 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,
%T 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,
%U 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
%N Expansion of Jacobi theta function theta_4(q^2).
%H G. C. Greubel, <a href="/A089798/b089798.txt">Table of n, a(n) for n = 0..5000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/JacobiThetaFunctions.html">Jacobi Theta Functions</a>
%H I. J. Zucker, <a href="http://dx.doi.org/10.1088/0305-4470/23/2/009">Further Relations Amongst Infinite Series and Products. II. The Evaluation of Three-Dimensional Lattice Sums</a>, J. Phys. A: Math. Gen. 23, 117-132, 1990.
%F 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
%t a[n_] := SeriesCoefficient[ EllipticTheta[4, 0, q^2], {q, 0, n}]; Table[a[n], {n, 0, 101}] (* _Jean-François Alcover_, Nov 12 2012 *)
%o (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
%Y Cf. A002448.
%K sign
%O 0,3
%A _Eric W. Weisstein_, Nov 12 2003
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