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

1,1

Links

Table of n, a(n) for n=1..21.

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

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)

Crossrefs

Cf. A292765.

Sequence in context: A365265 A166830 A072779 * A198014 A252592 A188577

Adjacent sequences: A292761 A292762 A292763 * A292765 A292766 A292767

Keyword

nonn,more

Author

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

Extensions

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

Name clarified by Paul Zimmermann, Oct 29 2017

Status

approved