Geodesic
Determinants containing powers of generalized Fibonacci numbers
Journal of integer sequences, Tome 19 (2016) no. 7
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},
     year = {2016},
     volume = {19},
     number = {7},
     zbl = {1383.11020},
     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/