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A127154
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Number of Dyck paths of semilength n and having no UDUD's starting at level 0; here U=(1,1), D=(1,-1).
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1
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1, 1, 1, 4, 11, 33, 105, 343, 1148, 3916, 13563, 47571, 168625, 603130, 2174041, 7889617, 28801737, 105696489, 389703392, 1442880489, 5362540760, 19998684400, 74815202891, 280685489717, 1055820378931, 3981166990632, 15045322802905
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| a(n)=A127153(n,0). Column 0 of A127153.
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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+z)/[1+z+2z^2+(1+z)sqrt(1-4z)].
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EXAMPLE
| a(3)=4 because we have UDUUDD, UUDDUD, UUDUDD and UUUDDD.
a(4)=11 because among the 14 (=A000108(4)) Dyck paths of semilength 4 the paths that do not qualify are UDUDUDUD, UDUDUUDD and UUDDUDUD.
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MAPLE
| g:=2*(1+z)/(1+z+2*z^2+sqrt(1-4*z)+z*sqrt(1-4*z)): gser:=series(g, z=0, 35): seq(coeff(gser, z, n), n=0..30);
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CROSSREFS
| Cf. A000108, A127153.
Sequence in context: A143787 A099159 A116394 * A062460 A098324 A144791
Adjacent sequences: A127151 A127152 A127153 * A127155 A127156 A127157
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 27 2007, Dec 13 2007
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