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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