This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A089798 #17 Feb 16 2025 08:32:51
%S A089798 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 A089798 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 A089798 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 A089798 Expansion of Jacobi theta function theta_4(q^2).
%H A089798 G. C. Greubel, <a href="/A089798/b089798.txt">Table of n, a(n) for n = 0..5000</a>
%H A089798 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/JacobiThetaFunctions.html">Jacobi Theta Functions</a>
%H A089798 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 A089798 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 A089798 a[n_] := SeriesCoefficient[ EllipticTheta[4, 0, q^2], {q, 0, n}]; Table[a[n], {n, 0, 101}] (* _Jean-François Alcover_, Nov 12 2012 *)
%o A089798 (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 A089798 Cf. A002448.
%K A089798 sign
%O A089798 0,3
%A A089798 _Eric W. Weisstein_, Nov 12 2003