A128202 Configuration of discs on pegs after n steps of the optimal solution to the Towers of Hanoi problem moving an odd number of discs from peg 0 to peg 2, or an even number from peg 0 to peg 1.

0, 2, 5, 4, 22, 21, 24, 26, 53, 52, 46, 45, 36, 38, 41, 40, 202, 201, 204, 206, 197, 196, 190, 189, 216, 218, 221, 220, 238, 237, 240, 242, 485, 484, 478, 477, 468, 470, 473, 472, 418, 417, 420, 422, 413, 412, 406, 405, 324, 326, 329, 328, 346, 345, 348, 350

Offset: 1

Author

Ralf Stephan, May 09 2007

Keywords

• base
• nonn

Comments

From Kevin Ryde, Oct 21 2021: (Start)

Configurations are encoded in ternary where the least significant digit is the peg number (0,1,2) which is the location of the smallest disc, the second least significant is the location of the second smallest disc, and so on.

This encoding and these configurations are as in A055661 except that the roles of pegs 1 and 2 are swapped, so ternary digit flip 1<->2, and so a(n) = A004488(A055661(n)).

(End)

Links

• Zoran Šunić, Tree morphisms, transducers and integer sequences, arXiv:math/0612080 [math.CO], 2006, see after proposition 5.4.
• Index entries for sequences related to Towers of Hanoi

Crossrefs

Cf. A007089 (ternary), A004488 (ternary 1<->2).

Cf. A055661 (pegs 1<->2).

Programs

PARI

a(n) = my(v=binary(bitxor(n,n>>1)),s=(-1)^#v,d=0); for(i=1,#v, if(v[i],d=(d+s)%3,s=-s); v[i]=d); fromdigits(v,3); \\ Kevin Ryde, Oct 21 2021

Extensions

Name and data corrected and extended by Kevin Ryde, Oct 21 2021