[seqfan] Re: square + n = triangle

[Max Alekseyev]

On Tue, Jun 30, 2009 at 8:16 AM, David Wilson<davidwwilson at comcast.net> wrote:
> Soluble for which n?

In other words, you want to solve:
x^2+ n = y(y+1)/2
or
(2y+1)^2 - 8x^2 = 8n+1
that is a generalized Pell equation. Possible integers at the right
hand side are listed in A035251.

Therefore, the sequence you are looking for are obtained from terms of
A035251 that are equal 1 modulo 8:

if m == 1 (mod 8) is in  A035251 then n = (m-1)/8 makes x^2+ n =
y(y+1)/2 solvable.

Regards,
Max