On the intersection of k-Lucas sequences and some binary sequences

For an integer k >= 2, let (L-n((k)))(n) be the k-generalized Lucas sequence which starts with 0, ... , 0, 2,1 (k terms) and each term afterwards is the sum of the k preceding terms. In this paper, we find all k-generalized Lucas numbers which are Fibonacci, Pell or Pell-Lucas numbers, i.e., we study the Diophantine equations L-n((k)) = F-m, L-n((k)) = P-m and L-n((k)) = Q(m) in positive integers n, m, k with k >= 3.