[seqfan] Re: Fixing A175155 Numbers n satisfying n^2 + 1 = x^2 y^3

[Georgi Guninski]

On Sat, Nov 17, 2012 at 08:04:58AM -0500, Neil Sloane wrote:
> I agree that 0 should be in the sequence. I added it and added the
> condition that x and y should be positive. The b-file is now wrong, since 0
> is missing, but I assume Bob Wilson will be changing it anyway when he
> responds to Georgi's comment.
> Neil
>

I wonder if there is some identity to generate terms from
known ones without Pell equations.

Generating powerfull solutions to x^2-1,x^2 is via a simple map
described in A060355.

Is there a powerful polynomial F(x) s.t. F(x) (x^2+1) - 1 = G(x)^2?