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A003446
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Triangulated (n+2)-gons rooted at one of the triangles.
(Formerly M1616)
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0
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0, 1, 1, 2, 6, 16, 52, 170, 579, 1996, 7021, 24892, 89214, 321994, 1170282, 4277352, 15715249, 57999700, 214939846, 799478680, 2983699498, 11169391168, 41929537871, 157807451672, 595340479694, 2250901216266, 8527700012092, 32369067177176
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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REFERENCES
| S. J. Cyvin, J. Brunvoll, E. Brendsdal, B. N. Cyvin and E. K. Lloyd, Enumeration of polyene hydrocarbons: a complete mathematical solution, J. Chem. Inf. Comput. Sci., 35 (1995) 743-751
F. Harary, E. M. Palmer and R. C. Read, On the cell-growth problem for arbitrary polygons, Discr. Math. 11 (1975), 371-389.
P. Lisonek, Closed forms for the number of polygon dissections. Journal of Symbolic Computation 20 (1995), 595-601.
R. C. Read, On general dissections of a polygon, Aequat. Math. 18 (1978), 370-388.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
P. K. Stockmeyer, The charm bracelet problem and its applications, pp. 339-349 of Graphs and Combinatorics (Washington, Jun 1973), Ed. by R. A. Bari and F. Harary. Lect. Notes Math., Vol. 406. Springer-Verlag, 1974.
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FORMULA
| Let c(x) = (1-sqrt(1-4*x))/(2*x) = g.f. for Catalans (A000108), let d(x) = 1+x*c(x^2). Then g.f. is (x/6)*(c^3+2*subs(x=x^3, c)+3*d*subs(x=x^2, c)).
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MATHEMATICA
| c[x_] = (1 - Sqrt[1 - 4*x])/(2*x); d[x_] = 1 + x*c[x^2]; f[x_] = (x/6)*(c[x]^3 + 2*c[x^3] + 3*d[x]*c[x^2]); CoefficientList[ Series[ f[x], {x, 0, 27}], x] (* From Jean-François Alcover, Sep 30 2011, after g.f. *)
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CROSSREFS
| Sequence in context: A002841 A136509 A100664 * A045696 A150028 A147730
Adjacent sequences: A003443 A003444 A003445 * A003447 A003448 A003449
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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