cp's OEIS Frontend

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.

A292341 Number of unrooted loops of length 2n on the square lattice that have winding number +1 around a fixed off-lattice point.

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%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