A174335 Upper bound in enumerating what majority decisions are possible with possible abstaining.

0, 16, 256, 2592, 24576, 240000, 2488320, 27659520, 330301440, 4232632320, 58060800000, 850068172800, 13243436236800, 218892235161600, 3827475696844800, 70614415872000000, 1371195958099968000

Offset

0,2

Comments

a(n) from last equations, Larson, p.22.

References

J. A. N. d. Condorcet. Essai sur l'application de l'analyse à la probabilité des décisions rendues à la pluralité des voix. L'imprimerie royale, Paris, 1785.

Links

Table of n, a(n) for n=0..16.

P. Erdos and L. Moser, On the representation of directed graphs as unions of orderings, Magyar Tud. Akad. Mat. Kutats Int. Kvzl., 9:125-132, 1964.

Paul Larson, Nick Matteo, Saharon Shelah, What majority decisions are possible with possible abstaining, arXiv:1003.2756 [math.CO], 2010.

S. Shelah, What majority decisions are possible, Discrete Mathematics, 309(8): 2349-2364, 2009.

Formula

a(n) = 16*(n^3)*(n!) = 16*A000578(n)*A000142(n).

a(n) = 16*A091363(n). - Michel Marcus, Jun 25 2015

Example

a(4) = 16*(4^3)*(4!) = 24576.

Mathematica

Table[16n^3 n!, {n, 0, 20}] (* Harvey P. Dale, Feb 25 2016 *)

Prog

(PARI) a(n) = 16*n^3*n! \\ Michel Marcus, Jun 25 2015

Crossrefs

Cf. A000142, A000578, A091363.

Sequence in context: A181215 A223666 A223617 * A297377 A283860 A223660

Adjacent sequences: A174332 A174333 A174334 * A174336 A174337 A174338

Keyword

easy,nonn

Author

Jonathan Vos Post, Mar 16 2010

Status

approved