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Search: id:A105641
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| A105641 |
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Number of hill-free Dyck paths of semilength n, having no UUDD's, where U=(1,1) and D=(1,-1) (a hill in a Dyck path is a peak at level 1). |
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+0
2
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| 0, 1, 2, 5, 14, 39, 111, 322, 947, 2818, 8470, 25677, 78420, 241061, 745265, 2315794, 7228702, 22656505, 71273364, 224965675, 712249471, 2261326010, 7197988973, 22966210236, 73437955105, 235307698544, 755395560220, 2429293941019
(list; graph; listen)
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OFFSET
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2,3
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COMMENT
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a(n)=A105640(n,0).
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REFERENCES
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E. Deutsch and L. Shapiro, A survey of the Fine numbers, Discrete Math., 241 (2001), 241-265.
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FORMULA
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G.f.=[(1+z)^2-sqrt((1+z^2)^2-4z)]/[2z(2+z+z^2)]-1.
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EXAMPLE
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a(4)=2 because we have UUDUDUDD and UUUDUDDD.
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MAPLE
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G:=((1+z)^2-sqrt((1+z^2)^2-4*z))/2/z/(2+z+z^2)-1: Gser:=series(G, z=0, 36): seq(coeff(Gser, z^n), n=2..32);
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CROSSREFS
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Cf. A118995.
Sequence in context: A132834 A000641 A026135 this_sequence A027035 A102406 A151409
Adjacent sequences: A105638 A105639 A105640 this_sequence A105642 A105643 A105644
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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), May 08 2006
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