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A005254 Number of weighted voting procedures.
(Formerly M2779 M2780)
3
1, 3, 9, 21, 51, 117, 271, 607, 1363, 3013, 6643, 14491, 31495, 67965, 146115, 312483, 666015, 1413915, 2992815, 6315135, 13292007, 27906585, 58464339, 122229123, 255072423, 531369483, 1105217223, 2295383319, 4760727375 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

M. Klamkin, ed., Problems in Applied Mathematics: Selections from SIAM Review, SIAM, 1990; see pp. 122-123.

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).

Solution to Board of Directors Problem, J. Rec. Math., 9 (No. 3, 1977), 240.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

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.

Solution to Board of Directors Problem, J. Rec. Math., 9 (No. 3, 1977), 240. (Annotated scanned copy)

MATHEMATICA

a[1, 1] = 1; a[n_, 1] := a[n, 1] = a[n - 1, Floor[(n + 1)/2]]; a[n_, k_ /; k > 1] := a[n, k] = a[n, 1] + a[n - 1, k - 1]; A005254 = Table[ Sum[ a[n, k], {k, 1, n}], {n, 1, 29}] (* Jean-François Alcover, Apr 03 2012, after recurrence of A037254 *)

PROG

(Haskell)

a005254 = sum . a037254_row  -- Reinhard Zumkeller, Nov 18 2012

CROSSREFS

Row sums of A037254.

Sequence in context: A111209 A262444 A109755 * A272265 A191796 A007056

Adjacent sequences:  A005251 A005252 A005253 * A005255 A005256 A005257

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from James A. Sellers, Feb 04 2000

STATUS

approved

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Last modified October 15 13:01 EDT 2018. Contains 316236 sequences. (Running on oeis4.)