A189769 Number of one-sided prudent walks from (0,0) to (n,n), with 3+n east steps, 3 west steps and n north steps.

2, 24, 200, 1400, 8820, 51744, 288288, 1544400, 8022300, 40646320, 201753552, 984312784, 4732273000, 22465296000, 105479913600, 490481598240, 2261264427180, 10345654242000, 47009200854000, 212283654382800, 953254695633240, 4258696302569280, 18936890673480000

Offset

1,1

Links

Georg Fischer, Table of n, a(n) for n = 1..170 [First 44 terms from Vincenzo Librandi]

S. Gao and H. Niederhausen, Sequences Arising From Prudent Self-Avoiding Walks, 2010.

Formula

a(n) = (n+1)*(2+n)*Gamma(2*n)/(3*(Gamma(n)^2).

Mathematica

Table[(n+1)*(2+n) Gamma[2*n]/(3 (Gamma[n])^2), {n, 30}] (* T. D. Noe, Apr 29 2011 *)

Prog

(Magma) [ Round((n+1)*(n+2)*Gamma(2*n)/(3*Gamma(n)^2)): n in [1..23] ]; // Klaus Brockhaus, Apr 29 2011

Crossrefs

Sequence in context: A121356 A052780 A245019 * A208533 A174668 A302444

Adjacent sequences: A189766 A189767 A189768 * A189770 A189771 A189772

Keyword

nonn,walk

Author

Shanzhen Gao, Apr 26 2011

Extensions

Extended by T. D. Noe, Apr 29 2011

a(45) and following corrected by Georg Fischer, Jul 27 2024

Status

approved