Author(s)

Sergio Falcon

Department of Mathematics and Institute for Applied Microelectronics (IUMA), University of Las Palmas de Gran Canaria (Spain).

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.

k–Fibonacci Numbers; k–Lucas Numbers; Generating Function

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.