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A114487
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Number of Dyck paths of semilength n having no UUDD's starting at level 0.
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1
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1, 1, 1, 3, 10, 31, 98, 321, 1078, 3686, 12789, 44919, 159407, 570704, 2058817, 7476621, 27310345, 100275628, 369886451, 1370066394, 5093778398, 19002602171, 71109895075, 266855940177, 1004045604976, 3786790901401, 14313706230574
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Column 0 of A114486.
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REFERENCES
| A. Sapounakis, I. Tasoulas and P. Tsikouras, Counting strings in Dyck paths, Discrete Math., 307 (2007), 2909-2924.
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FORMULA
| G.f.=2/[1+2z^2+sqrt(1-4z)].
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EXAMPLE
| a(3)=3 because we have UDUDUD, UUDUDD and UUUDDD, where U=(1,1), D=(1,-1).
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MAPLE
| G:=2/(1+2*z^2+sqrt(1-4*z)): Gser:=series(G, z=0, 33): 1, seq(coeff(Gser, z^n), n=1..30);
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CROSSREFS
| Cf. A114486.
Sequence in context: A068094 A100058 A002160 * A017934 A005510 A005725
Adjacent sequences: A114484 A114485 A114486 * A114488 A114489 A114490
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 30 2005
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