[seqfan] Sequence of squares whose first and second differences are squares?

[Georgi Guninski]

A question on mathoverflow [1] included this:

Is there an infinite integer sequence of squares whose first and second differences are squares?

Any ideas?

First differences only are easy.

If one ask about sequence of rational squares, there are infinitely many sequences such that the k-th differences are rational squares for all k:

p^2-q^2=u^2 (Pythagorean triples)
A=p/q
a(n)=A^(2*n)

[1] http://mathoverflow.net/questions/72040/how-many-sequences-of-rational-squares-are-there-all-of-whose-differences-are-al