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Search: id:A128725
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| A128725 |
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Number of skew Dyck paths of semilength n having no LL'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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+0
2
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| 1, 1, 3, 9, 30, 107, 399, 1537, 6069, 24434, 99924, 413943, 1733394, 7325471, 31203159, 133825441, 577418430, 2504681465, 10916208453, 47778816718, 209923718880, 925537620996, 4093530000888, 18157477014599, 80753894026905
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OFFSET
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0,3
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COMMENT
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a(n)=A128724(n,0).
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REFERENCES
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E. Deutsch, E. Munarini, and S. Rinaldi, Skew Dyck paths (in preparation).
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FORMULA
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G.f.=G=G(z) satisfies z^2*G^3-2zG^2+(1+z-z^2)G-1=0.
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EXAMPLE
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a(2)=3 because we have UDUD, UUDD, and UUDL; a(3)=9 because among the 10 skew Dyck paths of semilength 3 only UUUDLL does not qualify.
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MAPLE
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eq:=z^2*G^3-2*z*G^2+(1+z-z^2)*G-1=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. A128724.
Sequence in context: A024332 A036727 A053022 this_sequence A099783 A032125 A091699
Adjacent sequences: A128722 A128723 A128724 this_sequence A128726 A128727 A128728
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 31 2007
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