The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A005257 Number of weighted voting procedures. (Formerly M0716) 0
 2, 3, 5, 9, 17, 33, 64, 126, 249, 495, 984, 1962, 3913, 7815, 15608, 31194, 62346, 124650, 249216, 498348, 996531, 1992897, 3985464, 7970598, 15940542, 31880430, 63759552, 127517796, 255032987, 510063369, 1020121528, 2040237846, 4080465294, 8160920190 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Appears to satisfy a(1)=2, a(2)=3, a(3)=5 and, for n>3, a(n)=3a(n-1)-2a(n-2) if n is even and a(n)=a(n-1)+2a(n-2)-a([(n-1)/2]-1) if n is odd - John W. Layman, Jan 10 2000. 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 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. FORMULA Empirical g.f.: x*(x^16 +2*x^14 -12*x^13 +8*x^12 -6*x^11 +5*x^10 -3*x^7 +x^6 +9*x^5 -6*x^4 +3*x^3 -2*x^2 -3*x +2) / ((x -1)*(2*x -1)*(x^2 +1)*(2*x^2 -1)*(x^4 +1)*(2*x^4 -1)). - Colin Barker, Mar 16 2015 MATHEMATICA a={2, 3, 5}; For[i=4, i<35, i++, If[EvenQ[i], a=Append[a, 3 a[[i-1]]-2a[[i-2]]], a=Append[a, a[[i-1]]+2a[[i-2]]-a[[(i-1)/2-1]]]]]; a CROSSREFS Sequence in context: A049858 A092483 A324767 * A091697 A109740 A248155 Adjacent sequences:  A005254 A005255 A005256 * A005258 A005259 A005260 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS More terms from Vit Planocka (planocka(AT)mistral.cz), Sep 20 2002 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 10 17:00 EDT 2021. Contains 342852 sequences. (Running on oeis4.)