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A006343
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Arkons: number of elementary maps with n-1 nodes.
(Formerly M3400)
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3
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1, 0, 1, 1, 4, 10, 34, 112, 398, 1443, 5387, 20482, 79177, 310102, 1228187, 4910413, 19792582, 80343445, 328159601, 1347699906, 5561774999, 23052871229, 95926831442, 400587408251, 1678251696379, 7051768702245, 29710764875014
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OFFSET
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0,5
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REFERENCES
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K. Appel and W. Haken, Every planar map is four colorable. With the collaboration of J. Koch. Contemporary Mathematics, 98. American Mathematical Society, Providence, RI, 1989. xvi+741 pp. ISBN: 0-8218-5103-9.
F. R. Bernhart, Topics in Graph Theory Related to the Five Color Conjecture. Ph.D. Dissertation, Kansas State Univ., 1974.
F. R. Bernhart, Catalan, Motzkin and Riordan numbers, Discr. Math., 204 (1999) 73-112.
G. D. Birkhoff and D. C. Lewis, Chromatic polynomials. Trans. Amer. Math. Soc. 60, (1946). 355-451.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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_Reinhard Zumkeller_, Table of n, a(n) for n = 0..1000
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FORMULA
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a(n-1) = Sum (n-k-1)^(-1)*binomial(n, k)*binomial(2*n-3*k-4, n-2*k-2); k = 0..[ (n-2)/2 ], n >= 3.
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MATHEMATICA
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a[n_] := Sum[ Binomial[n, k]*Binomial[2*n-3*k-4, n-2*k-2]/(n-k-1), {k, 0, (n-2)/2}]; a[0] = 1; Table[a[n], {n, 0, 26}] (* Jean-François Alcover, Dec 14 2012, from formula *)
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PROG
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(Haskell)
a006343 0 = 1
a006343 n = sum $ zipWith div
(zipWith (*) (map (a007318 n) ks)
(map (\k -> a007318 (2*n - 3*k - 4) (n - 2*k - 2)) ks))
(map (toInteger . (n - 1 -)) ks)
where ks = [0 .. (n - 2) `div` 2]
-- Reinhard Zumkeller, Aug 23 2012
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CROSSREFS
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Cf. A000934.
Cf. A007318.
Sequence in context: A223006 A156700 A182645 * A149173 A149174 A222631
Adjacent sequences: A006340 A006341 A006342 * A006344 A006345 A006346
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KEYWORD
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easy,nonn,nice
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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Erroneously duplicated term 4 removed per Frank Bernhart's report Max Alekseyev, Feb 11 2010
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STATUS
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approved
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