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A128729
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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.
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1
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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
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0,3
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COMMENTS
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a(n)=A128728(n,0).
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LINKS
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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
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FORMULA
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G.f.=G=G(z) satisfies z^2*G^3-z(2-z)G^2+(1-z^2)G-1+z+z^2 =0.
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EXAMPLE
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a(2)=2 because we have UDUD and UUDD (UUDL does not qualify).
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MAPLE
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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);
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CROSSREFS
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Cf. A128728.
Sequence in context: A000707 A129777 A108600 * A006027 A049124 A163134
Adjacent sequences: A128726 A128727 A128728 * A128730 A128731 A128732
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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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