# Generating Functions, Weighted and Non-Weighted Sums for Powers of Second-Order Recurrence Sequences

@inproceedings{Stanica2000GeneratingFW, title={Generating Functions, Weighted and Non-Weighted Sums for Powers of Second-Order Recurrence Sequences}, author={Pantelimon St{\`u}anic{\`u}a}, year={2000} }

In this paper we find closed forms of the generating function 1 X k=0 U r nx n , for powers of

## 10 Citations

### Several Generating Functions for Second-Order Recurrence Sequences

- Mathematics
- 2009

This paper considers exponential and other types of generating functions for powers of second-order recurrence sequences and an extensive table of generating Functions for such sequences is provided.

### ON SUMS OF CERTAIN PRODUCTS OF LUCAS NUMBERS

- Mathematics
- 2009

New results about certain sums Sn(k) of products of the Lucas numbers are derived. These sums are related to the generating function of the k-th powers of the Fibonacci numbers. The sums for Sn(k)…

### Factorizations and representations of second order linear recurrences with indices in arithmetic progressions

- Mathematics
- 2009

Abstract : In this paper we consider second order recurrences {Vk} and {Un} We give second order linear recurrences for the sequences {V +/- kn} and {U +/-kn}. Using these recurrence relations, we…

### Weighted sums of some second-order sequences.

- Mathematics
- 2018

We derive weighted summation identities involving the second order recurrence sequence $\{w_n\} =\{ w_n(a,b; p, q)\}$ defined by $w_0 = a,\,w_1 = b;\,w_n = pw_{n - 1} - qw_{n - 2}\, (n \ge 2)$, where…

### ON SOME ASPECTS OF HORADAM SEQUENCE PERIODICITY VIA GENERATING FUNCTIONS

- Mathematics, Computer Science
- 2020

Sufficient conditions for cyclicity are stated and proved, using a new generating function approach, which address both nondegenerate and degenerate characteristic root cases, and consolidate the knowledge of, and recover, some previously observed periodic sequence behaviours which include the phenomenon of so called ‘masked’ cyclicity.

### Partial sums and generating functions of products of Horadam numbers with indices in arithmetic progression

- Mathematics
- 2019

The sums $\sum_{j = 0}^k {w_{rj + s} u_{mj + n} z^j }$, $\sum_{j = 0}^k {w_{rj + s} v_{mj + n} z^j }$ and $\sum_{j = 0}^k {w_{rj + s} w_{mj + n} z^j }$ are evaluated; where $r$, $s$, $k$, $m$ and $n$…

### Sums of Powers of Fibonacci and Lucas Polynomials in terms of Fibopolynomials

- Mathematics
- 2012

We study sums of powers of Fibonacci and Lucas polynomials of the form $% \sum_{n=0}^{q}F_{tsn}^{k}(x) $ and $\sum_{n=0}^{q}L_{tsn}^{k}% (x) $, where $s,t,k$ are given natural numbers, together with…

### Note on Ward-Horadam H(x) - binomials' recurrences and related interpretations, II

- Mathematics
- 2011

We deliver here second new $\textit{H(x)}-binomials'$ recurrence formula, were $H(x)-binomials' $ array is appointed by $Ward-Horadam$ sequence of functions which in predominantly considered cases…

### Unimodality, linear recurrences and combinatorial properties associated to rays in the generalized Delannoy matrix

- MathematicsJournal of Difference Equations and Applications
- 2019

In the present article, we give the explicit formulation of the linear recurrence sequence satisfied by the sum of the elements lying over any finite ray of the generalized Delannoy matrix, and find…

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