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Search: id:A135335
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| A135335 |
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Number of Dyck paths of semilength n having no DDUU's starting at level 2. |
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+0
2
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| 1, 1, 2, 5, 13, 36, 106, 327, 1045, 3433, 11529, 39414, 136733, 480180, 1703807, 6099193, 22000823, 79890801, 291808480, 1071403389, 3952020216, 14638293671, 54424065467, 203034222400, 759790586108, 2851348853311
(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)=A135329(n,0). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 13 2007
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REFERENCES
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A. Sapounakis, I. Tasoulas and P. Tsikouras, Counting strings in Dyck paths, Discrete Math., 307 (2007), 2909-2924.
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FORMULA
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G.f.=(1-2C+zC)/(2zC-Cz^2-C-z), where C=[1-sqrt(1-4z)]/(2z) is the g.f. of the Catalan numbers (A000108). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 13 2007
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EXAMPLE
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a(4)=13 because among the 14 (=A000108(4)) Dyck paths of semilength 4 only UUDDUUDD does not qualify.
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MAPLE
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g:=(1-2*C+z*C)/(2*z*C-C*z^2-C-z): C:=((1-sqrt(1-4*z))*1/2)/z: gser:=series(g, z=0, 30): seq(coeff(gser, z, n), n=0..25); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 13 2007
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CROSSREFS
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Cf. A000108, A135329.
Sequence in context: A135310 A135337 A133365 this_sequence A066723 A000994 A148296
Adjacent sequences: A135332 A135333 A135334 this_sequence A135336 A135337 A135338
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Dec 07 2007
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EXTENSIONS
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Edited and extended by Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 13 2007
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