0,2

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.

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].

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

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.

Table[(4^(n+1)+6n+5)/9, {n, 0, 24}]

(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)

Cf. A002450, A020988, A001045, A007583, A025579, A091841, A090822.

Sequence in context: A049179 A049154 A110136 this_sequence A066571 A087648 A086616

Adjacent sequences: A073721 A073722 A073723 this_sequence A073725 A073726 A073727

easy,nonn

Wouter Meeussen (wouter.meeussen(AT)pandora.be), Sep 01 2002