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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

Table of n, a(n) for n=2..29.

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.)