A292764 Minimal number of moves for the cyclic variant of Hanoi's tower for 4 pegs and n disks, with the final peg two steps away.

2, 8, 18, 36, 66, 120, 210, 360, 618, 1052, 1790, 3040, 5162, 8756, 14854, 25192, 42722, 72444, 122846, 208304, 353210

Offset: 1

Author

N. J. A. Sloane, Sep 27 2017, following a suggestion from Paul Zimmermann who computed the terms through a(16)

Keywords

• nonn
• more

Links

• Paul K. Stockmeyer, Variations on the Four-Post Tower of Hanoi Puzzle, Congressus Numerantium 102 (1994), pp. 3-12;
• Paul Zimmermann, Sage program
• Index entries for sequences related to Towers of Hanoi

Crossrefs

Cf. A292765.

Formula

Conjecture: for n >= 9, a(n) = a(n-1)+2*a(n-3)+c(n), where c(n) = 18 for odd n and c(n) = 14 for even n. - Paul Zimmermann, Oct 23 2017

Conjectures from Colin Barker, Oct 25 2017: (Start)

G.f.: 2*x*(1 + 3*x + 4*x^2 + 4*x^3 + 2*x^4 + 2*x^5 + 2*x^6 - 2*x^9) / ((1 - x)*(1 + x)*(1 - x - 2*x^3)).

a(n) = a(n-1) + a(n-2) + a(n-3) - 2*a(n-5) for n>10. [corrected by Paul Zimmermann, Oct 07 2020]

(End)

Extensions

Extended through a(21) by Paul Zimmermann, Oct 23 2017

Name clarified by Paul Zimmermann, Oct 29 2017