Meta-Fibonacci Sequences, Binary Trees, and Extremal Compact Codes

摘要

We look at a family of meta-Fibonacci sequences which arise in studying thenumber of leaves at the largest level in certain infinite sequences of binarytrees, restricted compositions of an integer, and binary compact codes. Forthis family of meta-Fibonacci sequences and two families of related sequenceswe derive ordinary generating functions and recurrence relations. Included inthese families of sequences are several well-known sequences in the OnlineEncyclopedia of Integer Sequences (OEIS).