Meta-Fibonacci Sequences, Binary Trees, and Extremal Compact Codes
Brad Jackson,
Department of Mathematics,
San Jose State University, USA.
Frank Ruskey,
Department of Computer Science,
University of Victoria, Canada.
Abstract:
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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Appears in Electronic Journal of Combinatorics,
13 (2006), #R26, 13 pages.
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Some corrections may be found
here (pdf)
or
here (ps).
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Selected citations:
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Nathaniel D. Emerson, "A Family of Meta-Fibonacci
Sequences Defined by Variable-Order Recursions",
Journal of Integer Sequences, Vol. 9 (2006),
Article 06.1.8, 21 pages.
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