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A382111 Maximum number of moves required to transition from the initial configuration (all disks on the first peg) to any possible configuration in the Towers of Hanoi puzzle with 4 pegs and n disks.

Original entry on oeis.org

0, 1, 3, 5, 9, 13, 17, 25, 33, 41, 49, 65, 81, 97, 113, 130, 161, 193, 225, 257, 294

Offset: 0

Geethan Pfeifer, Mar 16 2025

Values for n = 1..20 taken from Korf, 2004 (see table 2).
Somewhat surprisingly, this is not the same as A007664 from which first differs at a(15).
This gives a lower bound on the diameter of Hanoi graphs with k = 4.

Richard E. Korf, Best-first frontier search with delayed duplicate detection, In Proceedings of the 19th national conference on Artifical intelligence (AAAI'04). AAAI Press, (2004), 650-657.