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 A060589 2*(2^n-1)*3^(n-1). 2

%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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