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 A292341 #13 Oct 07 2019 05:44:58 %S A292341 1,16,232,3328,47957,696304,10187288,150087168,2224889247,33160970672, %T A292341 496608054904,7468314975488,112731489535747,1707278435651920, %U A292341 25932766975385096,394956591009678336,6029683178394959854,92254556123206383072 %N A292341 Number of unrooted loops of length 2n on the square lattice that have winding number +1 around a fixed off-lattice point. %C A292341 Here a rooted loop on the square lattice of length 2n is a sequence in Z^2 of length 2n such that (cyclically) consecutive pairs of points have distance 1. An unrooted loop is a rooted loop modulo cyclic permutations. %H A292341 Vaclav Kotesovec, <a href="/A292341/b292341.txt">Table of n, a(n) for n = 2..800</a> %H A292341 T. Budd, <a href="https://arxiv.org/abs/1709.04042">Winding of simple walks on the square lattice</a>, arXiv:1709.04042 [math.CO], 2017. %F A292341 G.f.: A(x) = q^2/(1-q^4) with q=q(16x) the Jacobi nome of parameter m=16x. %e A292341 For n=2 there is a(2)=1 such loop: the contour of the unit square (in counterclockwise direction). %t A292341 a[n_] := SeriesCoefficient[q^2/(1-q^4) /. q->EllipticNomeQ[16 x], {x,0,n}] %Y A292341 Cf. A005797. %K A292341 nonn,walk %O A292341 2,2 %A A292341 _Timothy Budd_, Sep 14 2017