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
Vaclav Kotesovec, Table of n, a(n) for n = 2..800
T. Budd, Winding of simple walks on the square lattice, arXiv:1709.04042 [math.CO], 2017.
FORMULA
G.f.: A(x) = q^2/(1-q^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/(1-q^4) /. q->EllipticNomeQ[16 x], {x, 0, n}]
CROSSREFS
KEYWORD
nonn,walk
AUTHOR
Timothy Budd, Sep 14 2017
STATUS
approved