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A005256 Number of weighted voting procedures.
(Formerly M2556)
2
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 (list; graph; refs; listen; history; text; internal format)
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) = 2a(n)-a([(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 A319445

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

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Last modified July 22 10:03 EDT 2019. Contains 325219 sequences. (Running on oeis4.)