Complete k-ary Trees and Generalized Meta-Fibonacci Sequences
Chris Deugau,
Department of Computer Science,
University of Victoria, Canada.
Frank Ruskey,
Department of Computer Science,
University of Victoria, Canada.
Abstract:
We show that a family of generalized meta-Fibonacci sequences
arise when counting the number of leaves at the largest level in certain
infinite sequences of k-ary trees and restricted compositions of
an integer.
For this family of generalized meta-Fibonacci sequences and two
families of related sequences we derive ordinary generating functions
and recurrence relations.
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Presented September 13 at the
Fourth Colloquium on Mathematics
and Computer Science: Algorithms, Trees, Combinatorics and Probabilities,
September 18-22, 2006, Institut Élie Cartan, Nancy, France, 2006.
DMTCS Proceedings Series, Volume AG, 203-214.
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