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A005257 Number of weighted voting procedures.
(Formerly M0716)
0

%I M0716

%S 2,3,5,9,17,33,64,126,249,495,984,1962,3913,7815,15608,31194,62346,

%T 124650,249216,498348,996531,1992897,3985464,7970598,15940542,

%U 31880430,63759552,127517796,255032987,510063369,1020121528,2040237846,4080465294,8160920190

%N Number of weighted voting procedures.

%C 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.

%D 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.

%D T. V. Narayana, Lattice Path Combinatorics with Statistical Applications. Univ. Toronto Press, 1979, pp. 100-101.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H G. Kreweras, <a href="http://www.numdam.org/item?id=MSH_1983__84__45_0">Sur quelques problèmes relatifs au vote pondéré</a>, [Some problems of weighted voting], Math. Sci. Humaines No. 84 (1983), 45-63.

%H B. E. Wynne & N. J. A. Sloane, <a href="/A002083/a002083_1.pdf">Correspondence, 1976-84</a>

%H B. E. Wynne & T. V. Narayana, <a href="/A002083/a002083_2.pdf">Tournament configuration, weighted voting, and partitioned catalans</a>, Preprint.

%H Bayard Edmund Wynne, and T. V. Narayana, <a href="http://www.numdam.org/item?id=BURO_1981__36__75_0">Tournament configuration and weighted voting</a>, Cahiers du bureau universitaire de recherche opérationnelle, 36 (1981): 75-78.

%F 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

%t 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

%K nonn,easy,nice

%O 1,1

%A _N. J. A. Sloane_

%E More terms from Vit Planocka (planocka(AT)mistral.cz), Sep 20 2002

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Last modified July 22 10:41 EDT 2019. Contains 325219 sequences. (Running on oeis4.)