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1, 8, 55, 364, 2380, 15504, 100947, 657800, 4292145, 28048800, 183579396, 1203322288, 7898654920, 51915526432, 341643774795, 2250829575120, 14844575908435, 97997533741800, 647520696018735, 4282083008118300
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Degree of variety K_{2,n}^1. Also number of double-rises (or odd-level peaks) in all generalized {(1,2),(1,-1)}-Dyck paths of length 3(n+1).
Number of dissections of a convex (2n+2)-gon by n-2 noncrossing diagonals into (2j+2)-gons, 1<=j<=n-1.
a(n) is the number of lattice paths avoiding $\uparrow ^{\geq 2}$ from $(0,0) $ to \ $(3n+1,n-1)$. [From Shanzhen Gao (shanzhengao(AT)yahoo.com), Apr 20 2010]
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REFERENCES
| M. S. Ravi et al., Dynamic pole assignment ..., SIAM J. Control Optimization, 34 (1996), 813-832, esp. p. 825.
Shanzhen Gao, Pattern Avoidance in Paths and Walks, in preparation [From Shanzhen Gao (shanzhengao(AT)yahoo.com), Apr 20 2010]
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FORMULA
| G.f.: g/((g-1)^3*(3*g-1)) where g*(1-g)^2 = x. - Mark van Hoeij, Nov 09 2011
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CROSSREFS
| Cf. A013699 (q=2), A013700 (q=3), A013701 (q=4), A013702 (q=5).
A column of triangle A102537.
Sequence in context: A179407 A026994 A110184 * A154245 A143420 A075734
Adjacent sequences: A013695 A013696 A013697 * A013699 A013700 A013701
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KEYWORD
| nonn,easy
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AUTHOR
| Joachim.Rosenthal(AT)nd.edu (Joachim Rosenthal), Emeric Deutsch (deutsch(AT)duke.poly.edu)
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