The number of valid factorizations of Fibonacci prefixes
arXiv:1806.09534 · doi:10.1016/j.tcs.2018.12.016
Abstract
We establish several recurrence relations and an explicit formula for V(n), the number of factorizations of the length-n prefix of the Fibonacci word into a (not necessarily strictly) decreasing sequence of standard Fibonacci words. In particular, we show that the sequence V(n) is the shuffle of the ceilings of two linear functions of n.
Version accepted to Theoretical Computer Science