Applied Mathematics

Volume 3, Issue 10 (October 2012)

ISSN Print: 2152-7385   ISSN Online: 2152-7393

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On the k–Lucas Numbers of Arithmetic Indexes

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DOI: 10.4236/am.2012.310175    6,682 Downloads   9,845 Views  Citations
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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.

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S. Falcon, "On the k–Lucas Numbers of Arithmetic Indexes," Applied Mathematics, Vol. 3 No. 10, 2012, pp. 1202-1206. doi: 10.4236/am.2012.310175.

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