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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Communication dans un congrès
Chassaing, Philippe and others. Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, 2006, Nancy, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, pp.203-214, 2006, DMTCS Proceedings
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Chris Deugau, Frank Ruskey. Complete k-ary trees and generalized meta-Fibonacci sequences. Chassaing, Philippe and others. Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, 2006, Nancy, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, pp.203-214, 2006, DMTCS Proceedings. 〈hal-01184719〉

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