A121924 Number of splitting steps that one can take with a sequence of n 2's.
0, 1, 1, 3, 4, 4, 7, 9, 10, 10, 14, 17, 19, 20, 20, 25, 29, 32, 34, 35, 35, 41, 46, 50, 53, 55, 56, 56, 63, 69, 74, 78, 81, 83, 84, 84, 92, 99, 105, 110, 114, 117, 119, 120, 120, 129, 137, 144, 150, 155, 159, 162, 164, 165, 165, 175, 184, 192, 199, 205, 210, 214, 217
Offset: 1
Keywords
Examples
a(11) = 14 from the formula, since b(11) = 5. From _Peter Kagey_, Sep 24 2017 (Start) For n = 8 an example of a(8) = 9 splitting steps is: [2 2 2 2 2 2 2 2] [3 2 2 2 2 2 2 1] [3 3 2 2 2 2 1 1] [3 3 3 2 2 1 1 1] [3 3 3 3 1 1 1 1] [4 3 3 2 1 1 1 1] [4 4 2 2 1 1 1 1] [4 4 3 1 1 1 1 1] [5 3 3 1 1 1 1 1] [5 4 2 1 1 1 1 1] (End)
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
- Robert F. Tichy and Stephan Wagner, Extremal Problems for Topological Indices in Combinatorial Chemistry.
- Stephan Wagner, Home page of Stephan G. Wagner.
- Stephan Wagner, Publications of Stephan G. Wagner
- Stephan Wagner, A class of trees and its Wiener index, Acta Applic. Mathem. 91 (2) (2006) 119-132.
- S. Wagner, Graph-theoretical enumeration and digital expansions: an analytic approach, Dissertation, Fakult. f. Tech. Math. u. Tech. Physik, Tech. Univ. Graz, Austria, Feb., 2006.
- S. Wagner and R. F. Tichy, Extremal problems for topological indices in combinatorial chemistry, J. of Computational Biology, vol. 12 (2005), pp. 1004-1013.
Crossrefs
Cf. A007318.
Programs
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Haskell
a121924 n = a007318 b 3 + (n - a007318 b 2) * (b*(b+3) - 2*(n+1)) `div` 4 where b = round $ sqrt $ 2 * fromIntegral n + 1/4 -- Reinhard Zumkeller, Sep 02 2013
Formula
a(n) = binomial(b(n),3) + (n-binomial(b(n),2))*(b(n)^2+3b(n)-2(n+1))/4, where b(n) = floor(sqrt(2n+1/4)+1/2) - Stephan Wagner (swagner(AT)sun.ac.za), Jul 18 2007
Extensions
Edited by Stephan Wagner (swagner(AT)sun.ac.za), Jul 18 2007
Comments