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A114500
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Number of Dyck paths of semilength n having no UUUDDD's starting at level zero; here U=(1,1), D=(1,-1). Also number of Dyck paths of semilength n having no UUDUDD's starting at level zero.
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1
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1, 1, 2, 4, 12, 37, 119, 390, 1307, 4460, 15452, 54207, 192170, 687386, 2477810, 8992007, 32825653, 120460613, 444125661, 1644324767, 6111002752, 22789116600, 85251100275, 319826371389, 1203008722282, 4536009027311, 17141555233270
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Column 0 of A114499.
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FORMULA
| G.f.=1/(1-zC+z^3), where C=[1-sqrt(1-4z)]/(2z) is the Catalan function.
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EXAMPLE
| a(4)=12 because among the 14 Dyck paths of semilength 4 only UDUUUDDD and UUUDDDUD contain UUUDDD starting at level 0.
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MAPLE
| C:=(1-sqrt(1-4*z))/2/z: G:=1/(1-z*C+z^3): Gser:=series(G, z=0, 35): 1, seq(coeff(Gser, z^n), n=1..30);
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CROSSREFS
| Cf. A114499.
Sequence in context: A111942 A003701 A193049 * A148212 A149844 A149845
Adjacent sequences: A114497 A114498 A114499 * A114501 A114502 A114503
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 04 2005
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