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%I M0716 #42 Nov 10 2023 08:51:32
%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