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 A105641 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). 1
 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; refs; listen; history; text; internal format)
 OFFSET 2,3 COMMENTS a(n) = A105640(n,0). LINKS E. Deutsch and L. Shapiro, A survey of the Fine numbers, Discrete Math., 241 (2001), 241-265. FORMULA G.f.: [(1+z)^2-sqrt((1+z^2)^2-4z)]/[2z(2+z+z^2)]-1. EXAMPLE a(4)=2 because we have UUDUDUDD and UUUDUDDD. MAPLE 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); CROSSREFS Cf. A118995. Sequence in context: A000641 A026135 A201778 * A027035 A102406 A307754 Adjacent sequences:  A105638 A105639 A105640 * A105642 A105643 A105644 KEYWORD nonn AUTHOR Emeric Deutsch, May 08 2006 STATUS approved

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Last modified November 27 12:23 EST 2020. Contains 338683 sequences. (Running on oeis4.)