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%I
%S 0,2,18,126,810,5022,30618,185166,1115370,6705342,40271418,241746606,
%T 1450833930,8706066462,52239587418,313447090446,1880711240490,
%U 11284353536382,67706379498618,406239051832686,2437436635519050
%N 2*(2^n-1)*3^(n-1).
%C a(n)/3^n is the expected time to finish a random Tower of Hanoi problem with n disks using optimal moves.
%H Harry J. Smith, <a href="/A060589/b060589.txt">Table of n, a(n) for n=0,...,200</a>
%H <a href="/index/Rea#recLCC">Index to sequences with linear recurrences with constant coefficients</a>, signature (9,-18).
%F a(n) =sum_{j<2^n}[j*A001316(j)] =6*a(n-1)+A008776(n-1) =4*A000400(n-1)-A008776(n-1) =A000244(n)*A060590(n)/A010684(n).
%F G.f.: 2*x/((3*x-1)*(6*x-1)). [_Colin Barker_, Dec 26 2012]
%o (PARI) { for (n=0, 200, write("b060589.txt", n, " ", 2*(2^n - 1)*3^(n - 1)); ) } [From _Harry J. Smith_, Jul 07 2009]
%Y Cf. A007798, A060586, A060590.
%K nonn,easy
%O 0,2
%A _Henry Bottomley_, Apr 05 2001
%E Corrected by _T. D. Noe_, Nov 07 2006
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