A189359 Number of homogeneous games for n players.
0, 1, 3, 8, 23, 76, 293, 1307, 6642, 37882
Offset: 0
Links
- 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
Comments