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A060590 Numerator of the expected time to finish a random Tower of Hanoi problem with n disks using optimal moves. 4
0, 2, 2, 14, 10, 62, 42, 254, 170, 1022, 682, 4094, 2730, 16382, 10922, 65534, 43690, 262142, 174762, 1048574, 699050, 4194302, 2796202, 16777214, 11184810, 67108862, 44739242, 268435454, 178956970, 1073741822, 715827882, 4294967294 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Harry J. Smith, Table of n, a(n) for n = 0..500

FORMULA

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

From Ralf Stephan, Mar 07 2003: (Start)

G.f.: (4*x^3+2*x^2+2*x)/(4*x^4-5*x^2+1).

a(n+4) = 5*a(n+2) - 4*a(n). (End)

EXAMPLE

a(2)=2 since there are nine equally likely possibilities, with times required of 0,1,1,2,2,3,3,3,3 giving an average of 18/9 = 2/1.

PROG

(PARI) a(n)={2*(2^n - 1)*(2 - (-1)^n)/3} \\ Harry J. Smith, Jul 07 2009

CROSSREFS

Denominator is A010684(n). a(2n)=A020988(n-1). Cf. A007798, A060586, A060589.

Sequence in context: A327930 A068511 A306544 * A129083 A045685 A045676

Adjacent sequences:  A060587 A060588 A060589 * A060591 A060592 A060593

KEYWORD

frac,nonn

AUTHOR

Henry Bottomley, Apr 05 2001

STATUS

approved

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Last modified November 22 00:32 EST 2019. Contains 329383 sequences. (Running on oeis4.)