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A372932
a(n) is the numerator of the expected number of restarts in the procedure described in A372422 if repeated until a single person has been selected.
1
1, 2, 29, 60, 181, 1098, 280183, 9540424, 314608765, 19504837446, 3802487264263, 22817278658868, 2943774725687279, 1037362763562236710, 3999657957457629563981, 2056075055857622080155312, 117203658895719313393625879, 154008310413390113443142533782, 1041844721074267325936152973816293
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
A372482 are the corresponding denominators.
Sequence in context: A115448 A276169 A107161 * A041097 A067071 A031918
KEYWORD
nonn,frac
AUTHOR
Hugo Pfoertner, May 17 2024
STATUS
approved