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Search: id:A100299
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| A100299 |
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Number of dissections of a convex n-gon by nonintersecting diagonals into an even number of regions. |
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2
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| 0, 2, 5, 23, 98, 452, 2139, 10397, 51524, 259430, 1323361, 6824435, 35519686, 186346760, 984400759, 5231789177, 27954506504, 150079713482, 809181079293, 4379654830223, 23787413800490, 129607968854732, 708230837732435
(list; graph; listen)
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OFFSET
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3,2
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REFERENCES
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P. Flajolet and M. Noy, Analytic combinatorics of non-crossing configurations, Discrete Math., 204, 1999, 203-229.
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FORMULA
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a(n)=sum(binom(n-3, 2k-1)*binom(n+2k-2, 2k-1)/(2k), k=1..floor((n-2)/2)). G.f.=(1/2)z^2/(1+z)+z/8-7z^2/8-(1/8)z*sqrt(1-6*z+z^2).
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EXAMPLE
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a(5)=5 because for a convex pentagon ABCDE we obtain dissections with an even number of regions by one of the following sets of diagonals: {AC}, {BD}, {CE}, {DA}, and {EB}.
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MAPLE
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a:=n->sum(binomial(n-3, 2*k-1)*binomial(n+2*k-2, 2*k-1)/2/k, k=1..floor((n-2)/2)): seq(a(n), n=3..33);
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CROSSREFS
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Cf. A100300.
Sequence in context: A023186 A023188 A106858 this_sequence A038833 A003501 A006990
Adjacent sequences: A100296 A100297 A100298 this_sequence A100300 A100301 A100302
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 12 2004
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