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Search: id:A143954
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| A143954 |
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Number of peaks in the peak plateaux of all Dyck paths of semilength n. A peak plateau is a run of consecutive peaks that is preceded by an upstep and followed by a down step; a peak consists of an upstep followed by a downstep. |
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+0
2
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| 0, 0, 1, 5, 19, 68, 243, 880, 3233, 12021, 45119, 170595, 648787, 2479057, 9509627, 36598497, 141246127, 546433952, 2118424887, 8227983472, 32010173957, 124715628852, 486550020967, 1900433894942, 7431033132717, 29085434212042
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OFFSET
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0,4
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COMMENT
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a(n) = Sum(k*A143953(n,k), k=0..n-1).
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FORMULA
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G.f. = z^2*C/[(1-z)^2*sqrt(1-4z)], where C=[1-sqrt(1-4z)]/(2z) is the Catalan function.
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EXAMPLE
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a(3)=5 because in the peak plateaux of the Dyck paths UDUDUD, UD(UUDD), (UUDD)UD, (UUDUDD) and U(UUDD)D, shown between parentheses, we have 0 + 1 + 1 + 2 + 1 = 5 peaks.
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MAPLE
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C:=((1-sqrt(1-4*z))*1/2)/z: G:=z^2*C/((1-z)^2*sqrt(1-4*z)): Gser:=series(G, z= 0, 30): seq(coeff(Gser, z, n), n=0..25);
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CROSSREFS
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A143952, A143953
Sequence in context: A001435 A092492 A070857 this_sequence A047145 A055991 A030662
Adjacent sequences: A143951 A143952 A143953 this_sequence A143955 A143956 A143957
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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 10 2008
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