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A128739
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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.
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1
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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
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OFFSET
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0,3
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COMMENTS
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a(n)=A128738(n,0).
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LINKS
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Table of n, a(n) for n=0..26.
E. Deutsch, E. Munarini, S. Rinaldi, Skew Dyck paths, J. Stat. Plann. Infer. 140 (8) (2010) 2191-2203
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FORMULA
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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.
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EXAMPLE
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a(3)=5 because we have UDUDUD, UDUUDL, UUUDLD, UUDUDL and UUUDLL.
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MAPLE
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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);
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CROSSREFS
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Cf. A128738.
Sequence in context: A159769 A159771 A159768 * A036766 A222589 A148322
Adjacent sequences: A128736 A128737 A128738 * A128740 A128741 A128742
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch, Mar 31 2007
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STATUS
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approved
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