On a Recurrence Relation Related to The Reve’s Puzzle (Journal of Bangladesh Academy of Sciences, 2018)
The 4-peg Tower of Hanoi problem, commonly known as the Reve’s puzzle, is well-known. Motivated by the optimality equation satisfied by the optimal value function M(n) satisfied in case of the Reve’s puzzle, (Matsuura et al. 2008) posed the following generalized recurrence relationT(n, a) = min {aT(n-t, a)+S(t,3)}            1≤ t ≤ nwhere n ≥ 1 and a ≥ 2 are integers, and S(t, 3) = 2t – 1 is the solution of the 3-peg Tower of Hanoi problem with t discs. Some local-value relationships are satisfied by T(n, a) (Majumdar et al. 2016). This paper studies the properties of  T(n+1, a) – T(n, a) more closely for the case when a is an integer not of the form 2i for any integer i ≥ 2.Journal of Bangladesh Academy of Sciences, Vol. 42, No. 2, 191-199, 2018