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