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 A006343 Arkons: number of elementary maps with n-1 nodes. (Formerly M3400) 3
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 REFERENCES 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). LINKS _Reinhard Zumkeller_, Table of n, a(n) for n = 0..1000 FORMULA 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. MATHEMATICA 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 *) PROG (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 CROSSREFS Cf. A000934. Cf. A007318. Sequence in context: A223006 A156700 A182645 * A149173 A149174 A222631 Adjacent sequences:  A006340 A006341 A006342 * A006344 A006345 A006346 KEYWORD easy,nonn,nice AUTHOR EXTENSIONS Erroneously duplicated term 4 removed per Frank Bernhart's report Max Alekseyev, Feb 11 2010 STATUS approved

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