OFFSET
1,1
COMMENTS
The number of walks on the simple square lattice that take one of the four directions U, D, R, L at each step and return to zero is zero if the number of steps is odd. If the number of steps is even, the sequence counts walks that start at (0,0), return to (0,0) and never pass through (0,0) or (1,0) in between.
LINKS
EXAMPLE
Example: a(1)=3 counts the walks UD, DU, LR (but not RL which would pass (1,0)) of 2 steps that return to the origin.
MAPLE
g002894 := hypergeom([1/2, 1/2], [1], 16*x^2) ;
g060150 := x*hypergeom([1, 3/2, 3/2], [2, 2], 16*x^2) ;
1-1/2/(g002894+g060150)-1/2/(g002894-g060150) ;
taylor(%, x=0, 40);
gfun[seriestolist](%) ; # includes zeros of odd steps
CROSSREFS
KEYWORD
nonn,walk
AUTHOR
R. J. Mathar, Sep 27 2020
STATUS
approved