An exponential Diophantine equation involving Narayana cow’s numbers

Abstract

Let (Cn)n≤0 be the Narayana cow‘s sequence given by C0 = Cfi = C2 = fi and Cn‡3 = Cn‡2 ‡ Cn for n ≤ O. In this paper, we are interested in finding all powers of two which are sums of two Narayana cow‘s numbers, i.e.,
we detemine all solutions of the exponential Diophantine equation Cm ‡ Cn = Xs in nonnegative integers n, m, and s ≤ X.