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A190512 Number of one-sided n-step prudent walks, avoiding single west step only, i.e., two or more consecutive west steps are permitted. 1
1, 2, 5, 11, 24, 53, 117, 258, 569, 1255, 2768, 6105, 13465, 29698, 65501, 144467, 318632, 702765, 1549997, 3418626, 7540017, 16630031, 36678688, 80897393, 178424817, 393528322, 867954037, 1914332891, 4222194104, 9312342245, 20539017381, 45300228866 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
S. Gao and H. Niederhausen, Sequences Arising From Prudent Self-Avoiding Walks, 2010.
FORMULA
a(n) = A052980(n+1). - R. J. Mathar, May 16 2011
G.f.: (1+x^2)/(1-2*x-x^3).
EXAMPLE
a(2)=5 since there are 5 such walks: WW, NN, EN, NE, EE.
PROG
(PARI) my(x='x+O('x^35)); Vec((1+x^2)/(1-2*x-x^3)) \\ Michel Marcus, Jun 28 2021
CROSSREFS
Cf. A110513 (essentially a signed version).
Sequence in context: A111297 A077864 A052980 * A110513 A018115 A242551
KEYWORD
nonn,walk
AUTHOR
Shanzhen Gao, May 11 2011
STATUS
approved

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Last modified April 20 02:51 EDT 2024. Contains 371798 sequences. (Running on oeis4.)