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Complete k-ary trees and generalized meta-Fibonacci sequences

Chris Deugau 1 Frank Ruskey 1
1 Department of Computer Science [Victoria]
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.
Keywords : Meta-Fibonacci sequence k-ary tree recurrence relation generating function ruler function.
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Chris Deugau, Frank Ruskey. Complete k-ary trees and generalized meta-Fibonacci sequences. Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, 2006, Nancy, France. pp.203-214. ⟨hal-01184719⟩

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