A005256 Number of weighted voting procedures.
1, 3, 6, 12, 23, 45, 87, 171, 336, 666, 1320, 2628, 5233, 10443, 20841, 41637, 83187, 166287, 332403, 664635, 1328934, 2657532, 5314398, 10628130, 21254940, 42508560, 85014492, 170026356, 340047479, 680089725, 1360169007, 2720327571
Offset: 1
References
- T. V. Narayana, Recent progress and unsolved problems in dominance theory, pp. 68-78 of Combinatorial mathematics (Canberra 1977), Lect. Notes Math. Vol. 686, 1978.
- T. V. Narayana, Lattice Path Combinatorics with Statistical Applications. Univ. Toronto Press, 1979, pp. 100-101.
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Links
- Herman Jamke, Table of n, a(n) for n = 1..60
- G. Kreweras, Sur quelques problèmes relatifs au vote pondéré, [Some problems of weighted voting], Math. Sci. Humaines No. 84 (1983), 45-63.
- B. E. Wynne & N. J. A. Sloane, Correspondence, 1976-84
- B. E. Wynne & T. V. Narayana, Tournament configuration, weighted voting, and partitioned catalans, Preprint.
- Bayard Edmund Wynne, and T. V. Narayana, Tournament configuration and weighted voting, Cahiers du bureau universitaire de recherche opérationnelle, 36 (1981): 75-78.
Programs
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Haskell
a005256 n = a005256_list !! (n-1) a005256_list = map (subtract 2) $ drop 3 a062178_list -- Reinhard Zumkeller, Nov 18 2012
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Mathematica
a[1] = 1; a[2] = 3; a[n_ /; n > 2] := a[n] = 2*a[n-1] - a[Floor[(n-3)/2]]; a[] = 0; Table[a[n], {n, 1, 32}] (* _Jean-François Alcover, Jul 30 2013, after Herman Jamke *)
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PARI
a(n)=if(n<3, (n>0)+2*(n>1), 2*a(n-1)-a((n-3)\2)) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 23 2008
Formula
a(n+1) = 2*a(n) - a(floor((n-2)/2)) starting with a(1)=1 and a(2)=3 (a(n)=0 if n<1). Also a(n) = A062178(n+2) - 2. - Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 23 2008
Extensions
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 23 2008