Sums of powers of Fibonacci polynomials

Prodinger, Helmut

doi:10.1007/s12044-009-0060-x

Cited by 6 publications

(2 citation statements)

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“…Name of sequence sums of second powers sums of third powers sums of powers Generalized Fibonacci [18,19,20,21,22,23] [ 24,25,26,27,28] [ 29,30,31] Generalized Tribonacci [32,33] Generalized Tetranacci [34,35] 2 AN APPLICATION OF THE…”

Section: Table 2 a Few Special Study On Sum Formulas Of Second Thirmentioning

confidence: 99%

On the Sums of Squares of Generalized Tribonacci Numbers: Closed Formulas of Σn k=0 xkW2

Soykan

2020

ACRI

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In this paper, closed forms of the sum formulas Σn k=0 xkW2 k ; Σn k=0 xk Σ Wk+1Wk and n k=0 xkWk+2Wk for the squares of generalized Tribonacci numbers are presented. As special cases, we give summation formulas of Tribonacci, Tribonacci-Lucas, Padovan, Perrin numbers and the other third order recurrence relations. We present the proofs to indicate how these formulas, in general, were discovered. Of course, all the listed formulas may be proved by induction, but that method of proof gives no clue about their discovery. Our work generalize third order recurrence relations.

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Section: Table 2 a Few Special Study On Sum Formulas Of Second Thirmentioning

confidence: 99%

On the Sums of Squares of Generalized Tribonacci Numbers: Closed Formulas of Σn k=0 xkW2

Soykan

2020

ACRI

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“…Name of sequence sums of second powers sums of third powers sums of powers Generalized Fibonacci [10,11,12,13,14,15,16,17,18] [19,20,21,22,23,24,25] [ 26,27,28,29] Generalized Tribonacci [30,31,32] Generalized Tetranacci [33,34,35] 2 An Application of the Sum of the Squares of the Numbers…”

Section: Table 2 a Few Special Study On Sum Formulas Of Second Thirmentioning

confidence: 99%

A Study on Generalized Tetranacci Numbers: Closed Form Formulas ∑n k=0 xkWk2 of Sums of the Squares of Terms

Soykan

2020

ARJOM

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Some new results for the ( p , q ) -Fibonacci and Lucas polynomials

Wang

2014

Adv Differ Equ

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In this paper, we investigate some arithmetic properties for the (p, q)-Fibonacci and Lucas polynomials associated with the classical Fibonacci and Lucas numbers. By applying some elementary methods and techniques, we establish some combinatorial identities for the (p, q)-Fibonacci and Lucas polynomials. It turns out that some known results in the references are obtained as special cases. MSC: 11B37; 05A19

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Sums of powers of Fibonacci polynomials

Abstract: Using the explicit (Binet) formula for the Fibonacci polynomials, a summation formula for powers of Fibonacci polynomials is derived straightforwardly, which generalizes a recent result for squares that appeared in

Cited by 6 publications

References 1 publication

On the Sums of Squares of Generalized Tribonacci Numbers: Closed Formulas of Σn k=0 xkW2

On the Sums of Squares of Generalized Tribonacci Numbers: Closed Formulas of Σn k=0 xkW2

A Study on Generalized Tetranacci Numbers: Closed Form Formulas ∑n k=0 xkWk2 of Sums of the Squares of Terms

Some new results for the ( p , q ) -Fibonacci and Lucas polynomials

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