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%I M2556 #36 Jan 31 2022 03:06:00
%S 1,3,6,12,23,45,87,171,336,666,1320,2628,5233,10443,20841,41637,83187,
%T 166287,332403,664635,1328934,2657532,5314398,10628130,21254940,
%U 42508560,85014492,170026356,340047479,680089725,1360169007,2720327571
%N Number of weighted voting procedures.
%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 Herman Jamke, <a href="/A005256/b005256.txt">Table of n, a(n) for n = 1..60</a>
%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 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
%t 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 *)
%o (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
%o (Haskell)
%o a005256 n = a005256_list !! (n-1)
%o a005256_list = map (subtract 2) $ drop 3 a062178_list
%o -- _Reinhard Zumkeller_, Nov 18 2012
%K nonn,easy,nice
%O 1,2
%A _N. J. A. Sloane_
%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 23 2008