JP Journal of Algebra, Number Theory and Applications
Volume 32, Issue 1, Pages 63 - 77
(February 2014)
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SUMS, PRODUCTS AND IDENTITIES INVOLVING k-FIBONACCI AND k-LUCAS SEQUENCES
http://dx.doi.org/10.17654/JPANTAFeb2014_063_077
P. Catarino, P. Vasco, A. Borges, H. Campos and A. P. Aires
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Abstract: In this paper, some basic properties of the k-Fibonacci and k-Lucas sequences are provided. Their relationship allows us to obtain some new properties involving sums and products of terms of these sequences. Furthermore, as a consequence of the Binet’s formula for each one, we also prove some identities involving these sequences. |
Keywords and phrases: Fibonacci numbers, Lucas numbers, k-Fibonacci numbers, k-Lucas numbers, Binet’s formula, recurrence relations. |
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