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 A166286 Number of Dyck paths with no UUU's and no DDD's, of semilength n having no peak plateaux (U=(1,1), D=(1,-1)). 1
 1, 1, 2, 3, 5, 9, 17, 34, 70, 147, 313, 673, 1459, 3185, 6995, 15445, 34265, 76342, 170744, 383214, 862814, 1948299, 4411167, 10011973, 22775773, 51920833, 118593423, 271376295, 622047011, 1428128025, 3283679333, 7560750299 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A peak plateau is a run of consecutive peaks that is preceded by an upstep U and followed by a down step D; a peak consists of an upstep followed by a downstep. LINKS FORMULA a(n) = A166285(n,0). G.f.: G(z) satisfies G = 1 + zG + z^2*G + z^3*G[G - 1/(1-z)]. EXAMPLE a(3)=3 because we have UDUDUD, UDUUDD, and UUDDUD (UUDUDD is a peak plateau). MAPLE F := RootOf(G = 1+z*G+z^2*G+z^3*G*(G-1/(1-z)), G): Fser := series(F, z = 0, 35): seq(coeff(Fser, z, n), n = 0 .. 32); CROSSREFS Cf. A166285. Sequence in context: A094373 A213705 A061902 * A179807 A110113 A137155 Adjacent sequences:  A166283 A166284 A166285 * A166287 A166288 A166289 KEYWORD nonn AUTHOR Emeric Deutsch, Oct 12 2009 STATUS approved

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Last modified August 17 07:13 EDT 2017. Contains 290635 sequences.