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

0, 2, 18, 126, 810, 5022, 30618, 185166, 1115370, 6705342, 40271418, 241746606, 1450833930, 8706066462, 52239587418, 313447090446, 1880711240490, 11284353536382, 67706379498618, 406239051832686, 2437436635519050, 14624626786683102, 87747781640805018

Offset

0,2

Comments

a(n)/3^n is the expected time to finish a random Tower of Hanoi problem with n disks using optimal moves.

Links

Harry J. Smith, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (9,-18).

Formula

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).

G.f.: 2*x/((3*x-1)*(6*x-1)). [Colin Barker, Dec 26 2012]

Mathematica

Table[2 (2^n - 1) 3^(n - 1), {n, 0, 50}] (* or *) LinearRecurrence[{9, -18}, {0, 2}, 40] (* Vincenzo Librandi, Jul 03 2018 *)

Prog

(PARI) a(n)={2*(2^n - 1)*3^(n - 1)} \\ Harry J. Smith, Jul 07 2009
(Magma) [2*(2^n - 1)*3^(n - 1): n in [0..30]]; // Vincenzo Librandi, Jul 03 2018

Crossrefs

Cf. A007798, A060586, A060590.

Sequence in context: A289830 A361304 A358952 * A325275 A277661 A367553

Adjacent sequences: A060586 A060587 A060588 * A060590 A060591 A060592

Keyword

nonn,easy

Author

Henry Bottomley, Apr 05 2001

Extensions

Corrected by T. D. Noe, Nov 07 2006

Status

approved