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Lucas generalized numbers in Narayana's cows sequence

Lucas generalized numbers in Narayana's cows sequence

Let {Nn}n≥0 be the Narayana's cows sequence given by N0 = 0, N1 = N2 = 1 and
 Nn+3 = Nn+2 + Nn, for integers n ≥ 0
 and let {Un}n ≥ 0 be the generalized Lucas sequence with parameters integers a ≥1, b =±1 given by U0 = 0, …