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A006078
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Number of triangulated (n+2)-gons rooted at an exterior edge.
(Formerly M3822)
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0
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1, 1, 5, 12, 45, 143, 511, 1768, 6330, 22610, 81818, 297160, 1086813, 3991995, 14733435, 54587280, 203000094, 757398510, 2834519142, 10637507400, 40023665682, 150946230006, 570534682710, 2160865067312, 8199711750100
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,3
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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
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
| Stockmeyer gives a g.f.
G.f.=[4(1-x-x^2)-(1-2x)(1-4x)^(1/2)-3(1-4x^2)^(1/2)]/(8x^2). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 19 2004
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MAPLE
| G:=(4*(1-x-x^2)-(1-2*x)*(1-4*x)^(1/2)-3*(1-4*x^2)^(1/2))/8/x^2: Gser:=series(G, x=0, 35): seq(coeff(Gser, x^n), n=2..28); (Deutsch)
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CROSSREFS
| Sequence in context: A052644 A052280 A195541 * A046612 A009425 A009416
Adjacent sequences: A006075 A006076 A006077 * A006079 A006080 A006081
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), E. K. Lloyd (E.K.Lloyd(AT)soton.ac.uk)
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 19 2004
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