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

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

2005-04-19

arxiv.org/abs/math/0504400v1

Mathematics

Combinatorics

13 pages, 3 figures

Scientific paper

We look at a family of meta-Fibonacci sequences which arise in studying the number of leaves at the largest level in certain infinite sequences of binary trees, restricted compositions of an integer, and binary compact codes. For this family of meta-Fibonacci sequences and two families of related sequences we derive ordinary generating functions and recurrence relations. Included in these families of sequences are several well-known sequences in the Online Encyclopedia of Integer Sequences (OEIS).

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