Tytuł artykułu
Autorzy
Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
In this paper we obtain explicit formulae for sums of products of a fixed number of consecutive generalized Fibonacci and Lucas numbers. These formulae are related to the recent work of Belbachir and Bencherif. We eliminate all restrictions about the initial values and the form of the recurrence relation. In fact, we consider six different groups of three sums that include alternating sums and sums in which terms are multiplied by binomial coefficients and by natural numbers. The proofs are direct and use the formula for the sum of the geometric series.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
Strony
247--258
Opis fizyczny
Bibliogr. 3 poz.
Twórcy
autor
- Kopernikova 7, 10010 Zagreb, Croatia, cerin@math.hr
Bibliografia
- [1] H. Belbachir, F. Bencherif, Sums of products of generalized Fibonacci and Lucas numbers, Ars Combinatoria, to appear.
- [2] A. T. Benjamin, J. J. Quinn, Proofs That Really Count, The Art of Combinatorial Proofs, Mathematical Association of America, Providence, RI, 2003.
- [3] E. Lucas, Théorie des Fonctions Numériques Simplement Périodiques, Amer. J.Math. 1 (1878), 184-240.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA5-0024-0003