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Part of 2023 Girls in Mathematics Tournament

Problems(1)

Is 2023 in the sequence?

Source: 2023 Girls in Mathematics Tournament, Level A, Problem 1

10/29/2023
Define (an)(a_n) a sequence, where a1=12,a2=24a_1= 12, a_2= 24 and for n≥3n\geq 3, we have: an=an−2+14a_n= a_{n-2}+14 a) Is 20232023 in the sequence? b) Show that there are no perfect squares in the sequence.
arithmetic sequencealgebranumber theory