A338089 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.

3, 10, 21, 40, 75, 134, 233, 400, 683, 1166, 1981, 3364, 5711, 9690, 16433, 27872, 47267, 80150, 135909, 230460, 390775

Offset

1,1

Links

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

Martin Ehrenstein, (C++) Program for A338024 (computes terms of this sequence, too)

Formula

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

Example

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).

Crossrefs

Cf. A292764, A338024.

Sequence in context: A146012 A027917 A038347 * A294365 A210980 A207380

Adjacent sequences: A338086 A338087 A338088 * A338090 A338091 A338092

Keyword

nonn,more

Author

Paul Zimmermann, Oct 09 2020

Extensions

a(17)-a(21) from Martin Ehrenstein, Oct 26 2020

Status

approved