A005254 Number of weighted voting procedures. (Formerly M2779 M2780)

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

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: A372559 A109755 A348403 * A272265 A191796 A367111

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