Journal of Integer Sequences, Vol. 18 (2015), Article 15.11.8

On a Matrix Arising from a Family of Iterated Self-Compositions

Martin Griffiths
Department of Mathematical Sciences
University of Essex
Colchester CO4 3SQ
United Kingdom


We obtain here a number of results associated with an infinite matrix arising from a family of iterated self-compositions. This matrix exhibits a rich structure, and our results include an intricate property of its rows, a characterization of its entries in terms of their Zeckendorf representations, and a link between its columns and a mathematical object known as the Fibonacci word.

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(Concerned with sequences A000201 A001588 A001611 A001612 A001950 A003622 A134859 A151915 A164485.)

Received March 27 2015; revised versions received October 25 2015; November 28 2015; December 11 2015. Published in Journal of Integer Sequences, December 16 2015.

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