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For an integer $k \geq 2$, let $\{ P_{n}^{(k)} \}_{n}$ be the $k$-generalizedPell sequence which starts with $0, \dots,0,1$($k$ terms) and each termafterwards is the sum of $k$ preceding terms. In this paper, we find all thesolutions of the Diophantine equation $P_{n}^{(k)} = N_{m}$ in non-negativeintegers $(n, k, m)$ with $k \geq 2$, where $\{ N_{m} \}_m$ is the Narayana'scows sequence. Our approach utilizes the lower bounds for linear forms inlogarithms of algebraic numbers established by Matveev, along with key insightsfrom the theory of continued fractions.

Common terms of generalized Pell and Narayana's cows sequences