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

1,2

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

Table of n, a(n) for n=1..56.

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

Prog

(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

Crossrefs

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

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

Sequence in context: A107732 A349475 A111364 * A319770 A229789 A357240

Adjacent sequences: A128199 A128200 A128201 * A128203 A128204 A128205

Keyword

base,nonn

Author

Ralf Stephan, May 09 2007

Extensions

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

Status

approved