This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A338089 #34 Aug 24 2025 19:06:11 %S A338089 3,10,21,40,75,134,233,400,683,1166,1981,3364,5711,9690,16433,27872, %T A338089 47267,80150,135909,230460,390775 %N 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. %H A338089 Martin Ehrenstein, <a href="/A338024/a338024.txt">(C++) Program for A338024</a> (computes terms of this sequence, too) %F A338089 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 %F A338089 a(n) ~ k*r^n, k = (725 + (310451786 - 3203949*sqrt(87))^(1/3) + (310451786 + 3203949*sqrt(87))^(1/3))/348, r=constant of A289265 (closed-form by Amiram Eldar via von Brömssen conjecture). - _Bill McEachen_, Aug 19 2025 %e A338089 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 A338089 Cf. A292764, A338024. %K A338089 nonn,more,changed %O A338089 1,1 %A A338089 _Paul Zimmermann_, Oct 09 2020 %E A338089 a(17)-a(21) from _Martin Ehrenstein_, Oct 26 2020