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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. 5
2, 8, 18, 36, 66, 120, 210, 360, 618, 1052, 1790, 3040, 5162, 8756, 14854, 25192, 42722, 72444, 122846, 208304, 353210 (list; graph; refs; listen; history; text; internal format)
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: A018229 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

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Last modified February 26 02:09 EST 2021. Contains 341619 sequences. (Running on oeis4.)