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A003408
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C(3n+6,n).
(Formerly M4643)
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4
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1, 9, 66, 455, 3060, 20349, 134596, 888030, 5852925, 38567100, 254186856, 1676056044, 11058116888, 73006209045, 482320623240, 3188675231420, 21094923659355, 139646485582065, 925029565741050, 6131164307078475
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Number of connected graphs without crossing edges on n+3 nodes on a circle and having exactly 1 interior face. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 06 2001
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REFERENCES
| C. Domb and A. J. Barrett, Enumeration of ladder graphs, Discrete Math. 9 (1974), 341-358.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Milan Janjic, Two Enumerative Functions
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EXAMPLE
| a(0)=1 because among the 4 non-crossing connected graphs on 3 nodes on a circle only the triangle has exactly 1 interior face.
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MAPLE
| a:=n->sum(binomial(2*n-2, n+j)*binomial(n-1, n-j), j=0..n): seq(a(n), n=3..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 29 2007
R := RootOf(x-t*(t-1)^2, t); ogf := series(1/((1-3*R)*(1-R)^6), x=0, 20); - Mark van Hoeij, Nov 08 2011
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CROSSREFS
| Sequence in context: A051375 A081902 A002695 * A037698 A037607 A055148
Adjacent sequences: A003405 A003406 A003407 * A003409 A003410 A003411
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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EXTENSIONS
| Formula found by Simon Plouffe (simon.plouffe(AT)gmail.com)
More terms from James A. Sellers (sellersj(AT)math.psu.edu), Aug 21 2000
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