login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A337870 The number of random walks on the simple square lattice that start at the origin (0,0) and pass through (1,0) after 2n+1 steps before having returned to the origin. 1

%I

%S 1,2,16,166,1934,24076,312906,4191822,57433950,800740450,11319707546,

%T 161841539812,2335765140994,33979681977530,497696233487200,

%U 7332776490675630,108595186409772174,1615573668169487898,24132221328987714066

%N The number of random walks on the simple square lattice that start at the origin (0,0) and pass through (1,0) after 2n+1 steps before having returned to the origin.

%C The number of walks that take one of the four directions U, D, R, L which arrive at (1,0) is zero if the number of steps is even. For odd number of steps we count the walks that start at (0,0) pass through any set of points that are not {(0,0),(1,0)} and arrive at (1,0).

%C The ordinary generating function is a mix of inverses of sums and differences of the hypergeometric generating functions in A002894 and A060150. See Maple.

%p g002894 := hypergeom([1/2,1/2],[1],16*x^2) ;

%p g060150 := x*hypergeom([1,3/2,3/2],[2,2],16*x^2) ;

%p 1/2/(g002894-g060150)-1/2/(g002894+g060150) ;

%p taylor(%,x=0,40);

%p L := gfun[seriestolist](%) ; # includes zeros of even steps

%Y Cf. A002894, A060150, A275912, A337869.

%K nonn,walk

%O 0,2

%A _R. J. Mathar_, Sep 27 2020

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 7 13:08 EST 2021. Contains 349581 sequences. (Running on oeis4.)