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Search: id:A166286
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| A166286 |
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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)). 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. |
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+0
2
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| 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; listen)
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OFFSET
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0,3
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COMMENT
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a(n) = A166285(n,0).
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FORMULA
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G.f. = G(z) satisfies G = 1 + zG + z^2*G + z^3*G[G - 1/(1-z)].
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EXAMPLE
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a(3)=3 because we have UDUDUD, UDUUDD, and UUDDUD (UUDUDD is a peak plateau).
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MAPLE
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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);
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CROSSREFS
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A166285
Sequence in context: A000051 A094373 A061902 this_sequence A110113 A137155 A014227
Adjacent sequences: A166283 A166284 A166285 this_sequence A166287 A166288 A166289
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 12 2009
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