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Kimberling, Clark; Komatsu, Takao; Liptai, Kálmán; Szalay, László

A connection between hyper-Fibonacci numbers and fissions of polynomial sequences. (English) Zbl 1448.11037

Fibonacci Q. 56, No. 3, 195-199 (2018).

Summary: We prove a new formula for hyper-, \(F^{[k]}_n\), using fissions of certain polynomials. The result is a concise description of the entries of the matrix of hyper-Fibonacci numbers.

© 2018 The Fibonacci Association

MSC:

11B39	Fibonacci and Lucas numbers and polynomials and generalizations
11D61	Exponential Diophantine equations

Cite Review PDF

Full Text: DOI Link

References:

[1]	Belbachir, H. and Belkhir, A., Combinatorial expressions involving Fibonacci, hyperfibonacci, and incomplete Fibonacci numbers, J. Integer Seq., 17 (2014), Article 14.4.3. · Zbl 1350.11017
[2]	Dil, A. and Mezo, I., A symmetric algorithm for hyperharmonic and Fibonacci numbers, Appl. Math. Comp., 206 (2008), 942-951. · Zbl 1200.65104
[3]	Kimberling, C., Fusion, fission, and factors, The Fibonacci Quarterly, 52.3 (2014), 195-202. · Zbl 1364.11042
[4]	Kimberling, C. and Szalay, L., t-sion of two polynomial sequences and factorization properties, The Fibonacci Quarterly, 54.1 (2016), 3-10. · Zbl 1400.11043
[5]	Komatsu, T. and Szalay, L., Explicit formula for hyper-Fibonacci numbers, and the equation F_x^[k] = F_y^[ℓ], Turkish J. Math, (2018), 993-1004. · Zbl 1424.11044

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.

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