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A060589
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2*(2^n-1)*3^(n-1).
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2
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0, 2, 18, 126, 810, 5022, 30618, 185166, 1115370, 6705342, 40271418, 241746606, 1450833930, 8706066462, 52239587418, 313447090446, 1880711240490, 11284353536382, 67706379498618, 406239051832686, 2437436635519050
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OFFSET
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0,2
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COMMENTS
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a(n)/3^n is the expected time to finish a random Tower of Hanoi problem with n disks using optimal moves.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=0,...,200
Index to sequences with linear recurrences with constant coefficients, signature (9,-18).
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FORMULA
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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]
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PROG
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(PARI) { for (n=0, 200, write("b060589.txt", n, " ", 2*(2^n - 1)*3^(n - 1)); ) } [From Harry J. Smith, Jul 07 2009]
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CROSSREFS
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Cf. A007798, A060586, A060590.
Sequence in context: A119578 A052610 A052653 * A064447 A043022 A057971
Adjacent sequences: A060586 A060587 A060588 * A060590 A060591 A060592
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KEYWORD
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nonn,easy
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AUTHOR
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Henry Bottomley, Apr 05 2001
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EXTENSIONS
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Corrected by T. D. Noe, Nov 07 2006
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STATUS
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approved
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