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A033275
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Number of diagonal dissections of an n-gon into 3 regions.
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4
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0, 5, 21, 56, 120, 225, 385, 616, 936, 1365, 1925, 2640, 3536, 4641, 5985, 7600, 9520, 11781, 14421, 17480, 21000, 25025, 29601, 34776, 40600, 47125, 54405, 62496, 71456, 81345, 92225, 104160, 117216
(list; graph; refs; listen; history; internal format)
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OFFSET
| 4,2
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COMMENTS
| Number of standard tableaux of shape (n-3,2,2) (n>=5). - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 13 2004
Number of short bushes with n+1 edges and 3 branch nodes (i.e. nodes with outdegree at least 2). A short bush is an ordered tree with no nodes of outdegree 1. Example: a(5)=5 because the only short bushes with 6 edges and 3 branch nodes are the five full binary trees with 6 edges. Column 3 of A108263. - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 29 2005
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REFERENCES
| D. Beckwith, Legendre polynomials and polygon dissections?, Amer. Math. Monthly, 105 (1998), 256-257.
F. R. Bernhart, Catalan, Motzkin and Riordan numbers, Discr. Math., 204 (1999) 73-112.
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FORMULA
| a(n)=binomial(n+1, 2)*binomial(n-3, 2)/3
G.f.: z^5*(5-4z+z^2)/(1-z)^5. - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 29 2005
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MATHEMATICA
| f[n_]:=n*(n+2)*(n+4)/3; s=0; lst={}; Do[AppendTo[lst, s+=f[n]], {n, 0, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 08 2009]
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CROSSREFS
| Cf. A033276.
Cf. A108263.
Sequence in context: A096942 A122244 A146854 * A166464 A059859 A146617
Adjacent sequences: A033272 A033273 A033274 * A033276 A033277 A033278
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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