2016/01/18 by Huang, Yuke, Wen, Zhiying
#11B85 #68Q45 #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.1601.04391
Let \cal P be the set of palindromes occurring in the Fibonacci sequence. In this note, we establish three structures of P and and discuss their properties: cylinder structure, chain structure and recursive structure. Using these structures, we determine that the number of distinct palindrome occurrences in \mathbbF[1,n] is exactly n, where \mathbbF[1,n] is the prefix of the Fibonacci sequence of length n. Then we give an algorithm for counting the number of repeated palindrome occurrences in \mathbbF[1,n], and get explicit expressions for some special n, which include the known results. We also give simpler proofs of some classical properties, such as in X.Droubay, W.F.Chuan and J.Shallit et al.