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Search: id:A097779
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| A097779 |
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Number of Motzkin paths of length n, starting with an up step, ending with a down step, and having no peaks (can be easily expressed using RNA secondary structure terminology). |
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+0
3
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| 1, 0, 0, 1, 1, 2, 5, 11, 25, 58, 135, 317, 750, 1785, 4272, 10275, 24823, 60210, 146576, 358010, 877087, 2154751, 5307166, 13102511, 32418806, 80375267, 199650310, 496803811, 1238276667, 3091173482, 7727893389, 19346109435, 48493869237
(list; graph; listen)
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OFFSET
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0,6
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FORMULA
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G.f. = z + (1-z)^2*[1-z+z^2-sqrt(1-2z-z^2-2z^3+z^4)]/(2z^2)
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EXAMPLE
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a(6)=5 because we have UHHHHD, UHDUHD, UUHHDD, UHUHDD, and UUHDHD, where U=(1,1), D=(1,-1) and H=(1,0).
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MAPLE
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G:=z+1/2*(1-z)^2/z^2*(1-z+z^2-sqrt(1-2*z-z^2-2*z^3+z^4)): Gser:=series(G, z=0, 40): 1, seq(coeff(Gser, z^n), n=1..37);
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CROSSREFS
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Cf. A004148.
Sequence in context: A006054 A106805 A094981 this_sequence A106336 A047775 A001432
Adjacent sequences: A097776 A097777 A097778 this_sequence A097780 A097781 A097782
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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), Sep 11 2004
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