2025 Fermat Problem 25

A sequence a_1, a_2,... has a_1 = 1, a_2 = 3 and a_n = -a_{n-1} + a_{n-2} for each integer n \ge 3. For example, a_3 = -a_2 + a_1 = -2. How many of the 2025 integers (a_1)^2, (a_2)^2, (a_3)^2,...,(a_{2025})^2 are divisible by 2025?

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Full credit to this problem is given to the CEMC, you may view all Fermat contests here.