Geodesic
Determinants containing powers of generalized Fibonacci numbers
Journal of integer sequences, Tome 19 (2016) no. 7.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 11B39, 11B20
Keywords: Fibonacci number, determinant, second-order recurrence, Catalan identity 
@article{JIS_2016__19_7_a7,
     author = {Tangboonduangjit, Aram and Thanatipanonda, Thotsaporn},
     title = {Determinants containing powers of generalized {Fibonacci} numbers},
     journal = {Journal of integer sequences},
     publisher = {mathdoc},
     volume = {19},
     number = {7},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2016__19_7_a7/}
}
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Tangboonduangjit, Aram; Thanatipanonda, Thotsaporn. Determinants containing powers of generalized Fibonacci numbers. Journal of integer sequences, Tome 19 (2016) no. 7. http://geodesic.mathdoc.fr/item/JIS_2016__19_7_a7/