Find all $n$ for which $3n^2+3n+1$ is a perfect square. Find all natural numbers $n$ for which $3n^2+3n+1$ is a perfect square.
I used discriminant method but failed. Then I found upper and lower bounds of this expression:
Lower:$(n+1)^2$
Upper:$(2n)^2$
But, this too does not seem to be useful. Please help me.

Using @J.G. 's observation, all solutions are generated by the following procedure.
From any solution e.g. $n=0,m=1$, one obtains a further solution as
$$(7n+4m+3,12n+7m+6).$$
