A005256 Number of weighted voting procedures. (Formerly M2556)

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

1,2

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.

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

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 *)

Prog

(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
(Haskell)
a005256 n = a005256_list !! (n-1)
a005256_list = map (subtract 2) $ drop 3 a062178_list
-- Reinhard Zumkeller, Nov 18 2012

Crossrefs

Sequence in context: A050243 A285262 A024505 * A097979 A215983 A339107

Adjacent sequences: A005253 A005254 A005255 * A005257 A005258 A005259

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 23 2008

Status

approved