This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A128739 Number of skew Dyck paths of semilength n having no DD'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 the path is defined to be the number of its steps. 1
 1, 1, 2, 5, 14, 41, 124, 386, 1230, 3992, 13150, 43856, 147796, 502530, 1721856, 5939353, 20608102, 71879003, 251876040, 886309559, 3130552258, 11095355269, 39447022648, 140645181280, 502773092420, 1801633916188, 6470373097004 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(n)=A128738(n,0). LINKS E. Deutsch, E. Munarini, S. Rinaldi, Skew Dyck paths, J. Stat. Plann. Infer. 140 (8) (2010) 2191-2203 FORMULA G.f.= G=G(t,z) satisfies z^2*G^3-z(1-z)G^2-(1-z)(1-3z)G+(1-z)^2=0. EXAMPLE a(3)=5 because we have UDUDUD, UDUUDL, UUUDLD, UUDUDL and UUUDLL. MAPLE eq:=z^2*G^3-z*(1-z)*G^2-(1-z)*(1-3*z)*G+(1-z)^2=0: G:=RootOf(eq, G): Gser:=series(G, z=0, 35): seq(coeff(Gser, z, n), n=0..30); CROSSREFS Cf. A128738. Sequence in context: A159769 A159771 A159768 * A036766 A222589 A148322 Adjacent sequences:  A128736 A128737 A128738 * A128740 A128741 A128742 KEYWORD nonn AUTHOR Emeric Deutsch, Mar 31 2007 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Puzzles | Hot | Classics
Recent Additions | More pages | Superseeker | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .