

A128729


Number of skew Dyck paths of semilength n with no UDL's.


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
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OFFSET

0,3


COMMENTS

A skew Dyck path is a path in the first quadrant which begins at the origin, ends on the xaxis, 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.


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) 21912203


FORMULA

a(n) = A128728(n,0).
G.f.: G = G(z) satisfies z^2*G^3  z(2z)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^3z*(2z)*G^2+(1z^2)*G1+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: A129777 A108600 A274484 * A006027 A049124 A275756
Adjacent sequences: A128726 A128727 A128728 * A128730 A128731 A128732


KEYWORD

nonn,changed


AUTHOR

Emeric Deutsch, Mar 31 2007


STATUS

approved



