A005245 conjecture

[David Wilson]

Also, if anyone is going to the trouble of computing 10^10 elements of 
A005245, maybe they could be saved for analysis without recomputation.

Also, the sequences smin(n) and pmin(n) might be worth adding to the OEIS.




My former colleague Toby Berger (now at U of Va)
has been looking at this problem.  Has anyone seen 
anything like this before?

%I A134939
%S A134939 0,2,64,1274,21760
%N A134939 Consider a 3-pole Tower of Hanoi configuration which begins with n rings on pole 1. Moves are made at random, where the 1-step transition probabilities out of any state are equal. Let e(n) be the expected number of transitions to reach the state in which which all rings are on pole 3. Sequence gives a(n), the numerator of e(n).
%C A134939 Both allowable transitions out of any of the three special states in which all the rings are on one of the poles have probabilty 1/2, and each of the three allowable transitions out of any of the other 3^n - 3 states have probabilty 1/3.
%C A134939 It appears that the denominator of e(n) for n>=1 is 3^(n-1).
%e A134939 The values of e(0), ..., e(4) are 0, 2, 64/3, 1274/9, 21760/27.
%K A134939 nonn,frac,more,new
%Y A134939 Cf. A134940.
%O A134939 0,2
%A A134939 Toby Berger (tb6n(AT)virginia.edu), Jan 23 2008

Neil