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

1,2

Links

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

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

Example

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.

Prog

(C++) See Martin Ehrenstein link, Oct 27 2020

Crossrefs

Cf. A292764, A338089.

Sequence in context: A134978 A115742 A026102 * A144519 A066995 A263896

Adjacent sequences: A338021 A338022 A338023 * A338025 A338026 A338027

Keyword

nonn,more

Author

Paul Zimmermann, Oct 07 2020

Extensions

a(17)-a(21) from Martin Ehrenstein, Oct 25 2020

Status

approved