%I #26 Dec 11 2020 06:15:59
%S 3,10,21,40,75,134,233,400,683,1166,1981,3364,5711,9690,16433,27872,
%T 47267,80150,135909,230460,390775
%N Minimal number of moves for the cyclic variant of Hanoi's tower for 4 pegs and n disks, with the final peg three steps away.
%H Martin Ehrenstein, <a href="/A338024/a338024.txt">(C++) Program for A338024</a> (computes terms of this sequence, too)
%F Conjecture: a(n) = a(n-1) + a(n-2) + a(n-3) - 2*a(n-5) for n > 9 (the same recurrence as conjectured in A292764 and A338024). - _Pontus von Brömssen_, Oct 12 2020
%e For n=2, assume the two disks are on North initially, first move the smallest one to South in 2 moves, then the largest one to East in 1 move, the smallest one back to North in 2 moves, the largest one to West in 2 moves, and finally the smallest one to West in 3 moves, with a total of 10 moves. Each disk has a number of moves which is 3 mod 4, thus a(n) == 3*n (mod 4).
%Y Cf. A292764, A338024.
%K nonn,more
%O 1,1
%A _Paul Zimmermann_, Oct 09 2020
%E a(17)-a(21) from _Martin Ehrenstein_, Oct 26 2020