Open AccessSums of products of generalized Fibonacci and Lucas numbers
Author(s) -
Zvonko Čerin
Publication year - 2009
Publication title -
demonstratio mathematica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.541
H-Index - 28
eISSN - 2391-4661
pISSN - 0420-1213
DOI - 10.1515/dema-2013-0167
Subject(s) - mathematics , fibonacci number , lucas number , binomial coefficient , lucas sequence , recurrence relation , fibonacci polynomials , pisano period , mathematical proof , natural number , series (stratigraphy) , combinatorics , discrete mathematics , pure mathematics , classical orthogonal polynomials , orthogonal polynomials , geometry , biology , paleontology
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.