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Search: id:A128730
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| A128730 |
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Number of UDL's in all skew Dyck paths of semilength n. 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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| 0, 0, 1, 4, 16, 68, 301, 1366, 6301, 29400, 138355, 655424, 3121438, 14930540, 71675839, 345148892, 1666432816, 8064278288, 39103576699, 189949958332, 924163714216, 4502711570988, 21966152501239, 107284324830302
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OFFSET
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0,4
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COMMENT
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a(n)=Sum(k*A128728(n,k),k>=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.=2z^2/[1-6z+5z^2+(1+z)sqrt(1-6z+5z^2)].
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EXAMPLE
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a(3)=4 because we have UDUUDL, UUUDLD, UUDUDL, and UUUDLL (the other six skew Dyck paths of semilength are the five Dyck paths and UUUDDL.
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MAPLE
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G:=2*z^2/(1-6*z+5*z^2+(1+z)*sqrt(1-6*z+5*z^2)): Gser:=series(G, z=0, 30): seq(coeff(Gser, z, n), n=0..26);
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CROSSREFS
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Cf. A128728.
Sequence in context: A024551 A091153 A089979 this_sequence A006319 A059606 A000303
Adjacent sequences: A128727 A128728 A128729 this_sequence A128731 A128732 A128733
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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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