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A190512
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Number of one-sided n-step prudent walks, avoiding single west step only, i.e., two or more consecutive west steps are permitted.
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1
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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
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: (1+x^2)/(1-2*x-x^3).
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EXAMPLE
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a(2)=5 since there are 5 such walks: WW, NN, EN, NE, EE.
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PROG
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(PARI) my(x='x+O('x^35)); Vec((1+x^2)/(1-2*x-x^3)) \\ Michel Marcus, Jun 28 2021
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CROSSREFS
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Cf. A110513 (essentially a signed version).
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KEYWORD
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nonn,walk
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AUTHOR
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STATUS
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approved
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