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Search: id:A135307
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| A135307 |
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Number of Dyck paths of semilength n that do not contain the string UDDU. |
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+0
2
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| 1, 1, 2, 4, 9, 23, 63, 178, 514, 1515, 4545, 13827, 42540, 132124, 413741, 1304891, 4141198, 13214815, 42375461, 136478383, 441285890, 1431925180, 4661485203, 15219836738, 49827678840, 163535624722, 537962562453, 1773437280323
(list; graph; listen)
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OFFSET
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0,3
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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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The Sapounakis et al. reference gives an explicit formula.
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MAPLE
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A135306 := proc(n, k) if n =0 then 1 ; else add((-1)^(j-k)*binomial(n-k, j-k)*binomial(2*n-3*j, n-j+1), j=k..floor((n-1)/2)) ; %*binomial(n, k)/n ; fi ; end: A135307 := proc(n) A135306(n, 0) ; end: for n from 0 to 30 do printf("%a, ", A135307(n)) ; od: - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 08 2007
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CROSSREFS
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Leading column of A135306.
Sequence in context: A127384 A058585 A001573 this_sequence A000083 A092668 A164039
Adjacent sequences: A135304 A135305 A135306 this_sequence A135308 A135309 A135310
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KEYWORD
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nonn,easy
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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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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 08 2007
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