Sum properties for the k-Lucas numbers with arithmetic indexes

Abstract

Fibonacci numbers are fascinating and their impact on the field of mathematics has been great. In this paper, mainly present formulas for the sums of k-Lucas numbers with indexes in an arithmetic sequence, say an+r, for fixed integers a and r (0 \leq r \leq a-1). Also the generating function evaluates and presents the alternating sum for the k-Lucas numbers with arithmetic index.