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Search: id:A128736
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| A128736 |
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Number of skew Dyck paths of semilength and having no LDU'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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+0
2
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| 1, 1, 3, 10, 35, 127, 474, 1810, 7043, 27839, 111503, 451640, 1847032, 7616692, 31637664, 132252886, 555967283, 2348920207, 9968617393, 42477135370, 181661283779, 779492777031, 3354893322350, 14479454240492, 62652100034380
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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a(n)=A128735(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 zG^3=(1-2z)(G-1)(2G-1).
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EXAMPLE
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a(4)=35 because among the 36 (=A002212(4)) skew Dyck paths of semilength 4 only UUUDLDUD has a LDU.
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MAPLE
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eq:=z*G^3=(1-2*z)*(G-1)*(2*G-1): 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. A128735.
Adjacent sequences: A128733 A128734 A128735 this_sequence A128737 A128738 A128739
Sequence in context: A047127 A114196 A078789 this_sequence A084781 A008984 A097148
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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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