OFFSET
2,2
EXAMPLE
a(n)/A372482(n): 1/2, 2/5, 29/76, 60/157, 181/470, 1098/2839, 280183/723752, 9540424/24660295, 314608765/814014962, 19504837446/50504034347, ...
Approximately 0.5, 0.4, 0.38158, 0.38217, 0.38511, 0.38676, 0.38713, 0.38687, 0.38649, 0.38620, 0.38607, 0.38606, 0.38612, 0.38621, 0.38629, 0.38636, 0.38639, 0.38640, 0.38639, 0.38636, 0.38633, 0.38630, 0.38628, 0.38626, 0.38625, 0.38624, 0.38624, 0.38624, 0.38625, 0.38626, 0.38627, 0.38629, 0.38630, 0.38631, ...
Results of 10^9 simulated random games, average results per game:
Persons Restarts
n expected observed coin tosses coin tosses / person
2 0.5 0.50002 4.0000 2.0000
3 0.4 0.39998 6.3999 2.1333
4 0.38158 0.38164 9.0531 2.2633
5 0.38217 0.38215 11.8216 2.3643
6 0.38511 0.38512 14.6217 2.4369
7 0.38676 0.38674 17.4144 2.4878
8 0.38713 0.38717 20.1945 2.5243
9 0.38687 0.38688 22.9638 2.5515
10 0.38649 0.38651 25.7301 2.5730
PROG
(PARI) a372932(n) = {my (np=n+1, M=matrix(np)); M[1, 1]=M[2, 2]=1; for (j=3, np, for (k=0, j-1, M[j, k+1]=binomial(j-1, k)/2^(j-1))); for (k=2, np, M[k, np]+=M[k, 1]); numerator(((1/(matid(n-1)-M[3..np, 3..np]))*M[3..np, 1..1])[n-1, 1])};
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Hugo Pfoertner, May 17 2024
STATUS
approved