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 A190569 Number of n-step one-sided prudent walks, avoiding single west steps and single east steps. 0
 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 (list; graph; refs; listen; history; text; internal format)
 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 A363143 A282913 Adjacent sequences: A190566 A190567 A190568 * A190570 A190571 A190572 KEYWORD nonn,walk AUTHOR Shanzhen Gao, May 12 2011 STATUS approved

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Last modified June 13 17:32 EDT 2024. Contains 373391 sequences. (Running on oeis4.)