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On the k–Lucas Numbers of Arithmetic Indexes
Department of Mathematics and Institute for Applied Microelectronics (IUMA), University of Las Palmas de Gran Canaria (Spain)
- 1 Department of Mathematics and Institute for Applied Microelectronics (IUMA), University of Las Palmas de Gran Canaria (Spain)
Applied Mathematics·Volume 03 (2012)·Pages 1202–1206·Published 11 October 2012·DOI10.4236/am.2012.310175
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Abstract
In this paper, we study the k–Lucas numbers of arithmetic indexes of the form an+r , where n is a natural number and r is less than r. We prove a formula for the sum of these numbers and particularly the sums of the first k-Lucas numbers, and then for the even and the odd k-Lucas numbers. Later, we find the generating function of these numbers. Below we prove these same formulas for the alternated k-Lucas numbers. Then, we prove a relation between the k–Fibonacci numbers of indexes of the form 2rn and the k–Lucas numbers of indexes multiple of 4. Finally, we find a formula for the sum of the square of the k-Fibonacci even numbers by mean of the k–Lucas numbers.
Keywordsk–Fibonacci Numbersk–Lucas NumbersGenerating Function
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