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A073724
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(4^(n+1)+6n+5)/9.
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8
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1, 3, 9, 31, 117, 459, 1825, 7287, 29133, 116515, 466041, 1864143, 7456549, 29826171, 119304657, 477218599, 1908874365, 7635497427, 30541989673, 122167958655, 488671834581, 1954687338283, 7818749353089, 31274997412311
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n)=number of times a disk is moved from peg 1 to peg 2 during a move of a tower of 2n or (2n-1) disks from peg 1 to peg 2 ("Tower of Hanoi"-problem). Binomial transform of A025579.
An approximation to A091841.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..170
F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and A. R. Wilks, A Slow-Growing Sequence Defined by an Unusual Recurrence, J. Integer Sequences, Vol. 10 (2007), #07.1.2.
F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and A. R. Wilks, A Slow-Growing Sequence Defined by an Unusual Recurrence [pdf, ps].
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FORMULA
| G.f.: (1-3x)/((1-4x)(1-x)^2).
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EXAMPLE
| moving a tower of 4 disks =2^4-1 moves, coded {1,0,5,1,2,3,1,0,5,4,2,5,1,0,5}. The move from peg 1 to peg 2 has code "0" and this occurs 3 times. For 3 disks we also find 3 zeros in {0,1,3,0,4,5,0}. Hence a(2)=3. The coding corresponds to the rank of the permutation {'from peg' 1, 'to peg' 2, 'by peg' 3} or {1,2,3} with rank 0.
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MATHEMATICA
| Table[(4^(n+1)+6n+5)/9, {n, 0, 24}]
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PROG
| (PARI) a(n)=(4*4^n+6*n+5)/9
(PARI) a(n)=polcoeff((1-3*x)/(1-4*x)/(1-x)^2+x*O(x^n), n)
(MAGMA) [(4^(n+1)+6*n+5)/9: n in [0..40] ]: // Vincenzo Librandi, Apr 28 2011
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CROSSREFS
| Cf. A002450, A020988, A001045, A007583, A025579, A091841, A090822.
Sequence in context: A151034 A151035 A151036 * A151037 A066571 A087648
Adjacent sequences: A073721 A073722 A073723 * A073725 A073726 A073727
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KEYWORD
| easy,nonn
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AUTHOR
| Wouter Meeussen (wouter.meeussen(AT)pandora.be), Sep 01 2002
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