Sums of products of generalized Fibonacci and Lucas numbers

• Autorzy: Cerin Z.
• Języki publikacji: EN

Abstrakty

EN

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

EN

Fibonacci numbers; Lucas numbers

PL

liczby Fibonacciego; liczby Lucasa

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2009
• Tom: Vol. 42, nr 2
• Strony: 247--258
• Opis fizyczny: Bibliogr. 3 poz.

Twórcy

autor

Cerin Z.

• Kopernikova 7, 10010 Zagreb, Croatia,

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.