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Search: id:A128752
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| A128752 |
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Number of ascents of length at least 2 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 its steps. An ascent in a path is a maximal sequence of consecutive U steps. |
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+0
3
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| 0, 0, 2, 9, 41, 189, 880, 4131, 19522, 92763, 442798, 2121795, 10200477, 49176639, 237661176, 1151032005, 5585185425, 27146751885, 132145210270, 644128990155, 3143590707235, 15358979381175, 75117256339240, 367723284610905
(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)=Sum(k*A128751(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.=(1/2)(1-2z)sqrt[(1-z)/(1-5z)]-1/2
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EXAMPLE
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a(2)=2 because we have UUDD and UUDL.
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MAPLE
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G:=(1/2)*(1-2*z)*sqrt((1-z)/(1-5*z))-1/2: Gser:=series(G, z=0, 30): seq(coeff(Gser, z, n), n=0..27);
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CROSSREFS
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Cf. A128751.
Adjacent sequences: A128749 A128750 A128751 this_sequence A128753 A128754 A128755
Sequence in context: A052322 A130767 A020698 this_sequence A074611 A020038 A056845
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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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