A190570 Number of n-step one-sided prudent walks, avoiding exactly two consecutive west steps and two consecutive east steps.

1, 3, 5, 13, 27, 63, 137, 309, 683, 1527, 3393, 7565, 16835, 37503, 83497, 185957, 414075, 922119, 2053393, 4572669, 10182643, 22675407, 50494905, 112445269, 250399915, 557606103, 1241711393, 2765119597, 6157538211, 13711985439

Offset

1,2

Links

Table of n, a(n) for n=1..30.

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

Formula

G.f.: x*(1+x-2*x^2+2*x^3)/(1-2*x-x^2+2*x^3-2*x^4).

Prog

(PARI) my(x='x+O('x^35)); Vec(x*(1+x-2*x^2+2*x^3)/(1-2*x-x^2+2*x^3-2*x^4)) \\ Michel Marcus, Jun 28 2021

Crossrefs

Sequence in context: A084173 A354951 A223645 * A337860 A000631 A026569

Adjacent sequences: A190567 A190568 A190569 * A190571 A190572 A190573

Keyword

nonn,walk

Author

Shanzhen Gao, May 12 2011

Status

approved