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A128729 Number of skew Dyck paths of semilength n with no UDL's. A skew Dyck path is a path in the first quadrant which begins at the origin, ends on the x-axis, consists of steps U=(1,1)(up), D=(1,-1)(down) and L=(-1,-1)(left) so that up and left steps do not overlap. The length of a path is defined to be the number of steps in it. 1
1, 1, 2, 6, 20, 71, 262, 994, 3852, 15183, 60686, 245412, 1002344, 4129012, 17135432, 71575350, 300690836, 1269662127, 5385593406, 22938095326, 98059308676, 420610907183, 1809690341366, 7808145901068, 33776362530776 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n)=A128728(n,0).

LINKS

Table of n, a(n) for n=0..24.

E. Deutsch, E. Munarini, S. Rinaldi, Skew Dyck paths, J. Stat. Plann. Infer. 140 (8) (2010) 2191-2203

FORMULA

G.f.=G=G(z) satisfies z^2*G^3-z(2-z)G^2+(1-z^2)G-1+z+z^2 =0.

EXAMPLE

a(2)=2 because we have UDUD and UUDD (UUDL does not qualify).

MAPLE

eq:=z^2*G^3-z*(2-z)*G^2+(1-z^2)*G-1+z+z^2=0: G:=RootOf(eq, G): Gser:=series(G, z=0, 30): seq(coeff(Gser, z, n), n=0..27);

CROSSREFS

Cf. A128728.

Sequence in context: A000707 A129777 A108600 * A006027 A049124 A163134

Adjacent sequences:  A128726 A128727 A128728 * A128730 A128731 A128732

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Mar 31 2007

STATUS

approved

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Last modified November 27 15:41 EST 2014. Contains 250224 sequences.