A292764 - OEIS

%I #46 Nov 23 2024 18:15:01

%S 2,8,18,36,66,120,210,360,618,1052,1790,3040,5162,8756,14854,25192,

%T 42722,72444,122846,208304,353210

%N 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.

%H Paul K. Stockmeyer, <a href="http://www.cs.wm.edu/~pkstoc/boca.pdf">Variations on the Four-Post Tower of Hanoi Puzzle</a>, Congressus Numerantium 102 (1994), pp. 3-12;

%H Paul Zimmermann, <a href="/A292764/a292764.txt">Sage program</a>

%H <a href="/index/To#Hanoi">Index entries for sequences related to Towers of Hanoi</a>

%F 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

%F Conjectures from _Colin Barker_, Oct 25 2017: (Start)

%F 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)).

%F 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]

%F (End)

%Y Cf. A292765.

%K nonn,more

%O 1,1

%A _N. J. A. Sloane_, Sep 27 2017, following a suggestion from _Paul Zimmermann_ who computed the terms through a(16).

%E Extended through a(21) by _Paul Zimmermann_, Oct 23 2017

%E Name clarified by _Paul Zimmermann_, Oct 29 2017