A189359 Number of homogeneous games for n players.

0, 1, 3, 8, 23, 76, 293, 1307, 6642, 37882

Offset

0,3

Links

Table of n, a(n) for n=0..9.

I. Krohn and P. Sudhölter, Directed and weighted majority games, Mathematical Methods of Operation Research, 42, 2 (1995), 189-216. See Table 1, p. 213; also on ResearchGate.

P. Sudhölter, Homogeneous games as anti step functions, International Journal of Game Theory Vol. 18, (1989), 433-469.

Formula

Conjecture: g.f.: Q(0)*x/(1-x), where Q(k) = 1 + (1-(1-x)^(2*k+2))/(1- (1-(1-x)^(2*k+3))/(1-(1-x)^(2*k+3) + 1/Q(k+1))); (continued fraction). - Sergei N. Gladkovskii, May 13 2013

Note that a(n) - a(n-1) = A022493(n) for 1 <= n <= 9. Does this equality hold for n > 9? If so, then we have the g.f. 1/(1 - x)*( Sum_{n >= 1} Product_{k = 1..n} (1 - (1 - x)^k) ). - Peter Bala, Dec 13 2021

Crossrefs

Subclass of A000617. Cf. A001532, A022493, A109456, A132183.

Sequence in context: A099265 A099266 A024716 * A125782 A343176 A307875

Adjacent sequences: A189356 A189357 A189358 * A189360 A189361 A189362

Keyword

nonn,hard,more

Author

Fabián Riquelme, Apr 20 2011

Status

approved