Related to this question : Find three arithmetic progressions of three square numbers
I am looking for a sequence $$a_1,a_2,\cdots a_n$$ forming an arithmetic progression such that all the $a_j$ are perfect squares, an example with $3$ entries is $$49,169,289$$ However, the next term would be $409$ , not being a perfect square.
Can the index $n$ be aqrbitary large ? In other words, can the sequence be arbitary long ? If not, what is the maximum possible value for $n$ ?