Some Local-Value Relationships for the Recurrence Relation Related to the Tower of Hanoi Problem: Some Local-Value Relationships for the Recurrence Relation Related to the Tower of Hanoi Problem - MAJUMDAR, Abdullah-Al-Kafi (Proceedings of the Pakistan Academy of Sciences: A. Physical and Computational Sciences, 2021)
Motivated by the recurrence relation satisfied by the 4-peg tower of the Hanoi Problem, Matsuura [1] has considered the generalized recurrence relation of the form 1 t n T(n, , ) min T(n t, , ) S(t,3) , = − + where and are natural numbers, and S(t, 3) = 2t – 1 is the solution of the 3-peg Tower of Hanoi problem with t discs. This paper studies more closely the above recurrence relation and gives some new relationships, including some local-value relationships. The Reve’s puzzle is a particular case of the above recurrence relation with = 2.