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A005257 Number of weighted voting procedures.
(Formerly M0716)
0
2, 3, 5, 9, 17, 33, 64, 126, 249, 495, 984, 1962, 3913, 7815, 15608, 31194, 62346, 124650, 249216, 498348, 996531, 1992897, 3985464, 7970598, 15940542, 31880430, 63759552, 127517796, 255032987, 510063369, 1020121528, 2040237846, 4080465294, 8160920190 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

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

Table of n, a(n) for n=1..34.

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

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

MATHEMATICA

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

CROSSREFS

Sequence in context: A080889 A049858 A092483 * A091697 A109740 A248155

Adjacent sequences:  A005254 A005255 A005256 * A005258 A005259 A005260

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

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

STATUS

approved

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Last modified November 13 13:15 EST 2018. Contains 317149 sequences. (Running on oeis4.)