A338024 Minimal number of moves for the cyclic variant of Hanoi's tower for 4 pegs and n disks, with the final peg one step away.
1, 6, 15, 28, 57, 98, 179, 304, 521, 894, 1519, 2576, 4381, 7434, 12603, 21380, 36265, 61486, 104263, 176808, 299797
Offset: 1
Examples
For n=2, assume the two disks are on North initially, first move the smallest one to West in 3 moves, then the largest one to East in 1 move, and the smallest one to East also in 2 moves, with a total of 6 moves. Each disk has a number of moves which is 1 mod 4, thus a(n) = n mod 4.
Links
- Martin Ehrenstein, (C++) Program
Formula
Conjecture: a(n) = a(n-1) + a(n-2) + a(n-3) - 2*a(n-5) for n > 11.
Conjectured g.f.: x*(1+5*x+8*x^2+6*x^3+8*x^4+8*x^6-4*x^8+4*x^9-4*x^10)/((1-x)*(1+x)*(1-x-2*x^3)). - Stefano Spezia, Oct 07 2020 after Paul Zimmermann
Extensions
a(17)-a(21) from Martin Ehrenstein, Oct 25 2020