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 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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. LINKS E. Deutsch, E. Munarini, S. Rinaldi, Skew Dyck paths, J. Stat. Plann. Infer. 140 (8) (2010) 2191-2203 FORMULA a(n) = A128728(n,0). 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: 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

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Last modified July 23 16:56 EDT 2017. Contains 289690 sequences.