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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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10
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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;
text;
internal format)
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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).
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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LINKS
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P. J. 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. [Scanned annotated and corrected copy]
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FORMULA
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Stockmeyer gives a g.f.
G.f.: (4*(1-x-x^2)-(1-2*x)(1-4*x)^(1/2)-3(1-4*x^2)^(1/2))/(8*x^2). - Emeric Deutsch, 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); # Emeric Deutsch, Dec 19 2004
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MATHEMATICA
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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, 26}]; Drop[ CoefficientList[gser, x], 2] (* Jean-François Alcover, Apr 06 2012, after Emeric Deutsch *)
Drop[CoefficientList[Series[(4(1-x-x^2)- (1-2x)Sqrt[1-4x]- 3Sqrt[1- 4x^2])/(8x^2), {x, 0, 30}], x], 2] (* Harvey P. Dale, Apr 07 2013 *)
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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