A190569 Number of n-step one-sided prudent walks, avoiding single west steps and single east steps.

1, 1, 3, 7, 13, 25, 51, 103, 205, 409, 819, 1639, 3277, 6553, 13107, 26215, 52429, 104857, 209715, 419431, 838861, 1677721, 3355443, 6710887, 13421773, 26843545, 53687091, 107374183, 214748365, 429496729, 858993459, 1717986919, 3435973837

Offset

0,3

Links

Table of n, a(n) for n=0..32.

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

Index entries for linear recurrences with constant coefficients, signature (2,-1,2).

Formula

a(n) = A007909(n+2).

G.f.: (1-x+2*x^2)/((1-2*x)*(1+x^2)).

Prog

(PARI) my(x='x+O('x^35)); Vec((1-x+2*x^2)/((1-2*x)*(1+x^2))) \\ Michel Marcus, Jun 28 2021

Crossrefs

Essentially a duplicate of A007909.

Sequence in context: A275788 A169914 A078000 * A007909 A376448 A363143

Adjacent sequences: A190566 A190567 A190568 * A190570 A190571 A190572

Keyword

nonn,walk

Author

Shanzhen Gao, May 12 2011

Status

approved