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Search: id:A006078
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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
1
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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; listen)
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OFFSET
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2,3
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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
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
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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
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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
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Sequence in context: A129795 A052644 A052280 this_sequence A046612 A009425 A009416
Adjacent sequences: A006075 A006076 A006077 this_sequence A006079 A006080 A006081
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), E. K. Lloyd (E.K.Lloyd(AT)soton.ac.uk)
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 19 2004
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