

A292341


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


1



1, 16, 232, 3328, 47957, 696304, 10187288, 150087168, 2224889247, 33160970672, 496608054904, 7468314975488, 112731489535747, 1707278435651920, 25932766975385096, 394956591009678336, 6029683178394959854, 92254556123206383072
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OFFSET

2,2


COMMENTS

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.


LINKS



FORMULA

G.f.: A(x) = q^2/(1q^4) with q=q(16x) the Jacobi nome of parameter m=16x.


EXAMPLE

For n=2 there is a(2)=1 such loop: the contour of the unit square (in counterclockwise direction).


MATHEMATICA

a[n_] := SeriesCoefficient[q^2/(1q^4) /. q>EllipticNomeQ[16 x], {x, 0, n}]


CROSSREFS



KEYWORD

nonn,walk


AUTHOR



STATUS

approved



