Some local-value relationships for the recurrence relation related to the tower of hanoi problem

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 (formula presented) where α and β 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 α = 2. © pakistan academy of sciences.