Square number + square number = square number

Does there exist an infinitely long sequence (\(a_1, a_2, a_3, \dots\)), where each term of the sequence is a perfect square, \(a_n<a_{n+1}\) is true for any positive integer \(n\) and \(a_k+a_{k+1}\) is a perfect square for any positive integer \(k\)?

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