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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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2
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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; refs; listen; history; internal format)
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OFFSET
| 0,6
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FORMULA
| 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
| 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
| 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
| Cf. A004148.
Sequence in context: A006054 A106805 A094981 * A106336 A047775 A001432
Adjacent sequences: A097776 A097777 A097778 * A097780 A097781 A097782
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Sep 11 2004
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