Journal of Integer Sequences, Vol. 19 (2016), Article 16.7.1

Determinants Containing Powers of Generalized Fibonacci Numbers

Aram Tangboonduangjit and Thotsaporn Thanatipanonda
Mahidol University International College
Nakhonpathom 73170


We study the determinants of matrices whose entries are powers of the Fibonacci numbers. We then extend the results to include entries that are powers of a second-order linear recurrence relation. These results motivate a fundamental identity of determinants whose entries are powers of linear polynomials. Finally, we discuss the determinants of matrices whose entries are products of the general second-order linear recurrence relations.

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(Concerned with sequences A000045.)

Received February 10 2016; revised versions received June 20 2016; July 16 2016. Published in Journal of Integer Sequences, August 29 2016.

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