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Help with While Loop Function

Please Help me to Get the following to work as desired
t is the triangular number. I increment it repeated ly by adding the
counter x to it. When t*((y^2+1)/2)^2 + y^2 is a perfect square i want
to append t to my list of trangular numbers with the list starting
with {0,1}, and exit the loop when 3 more triangular numbers have been
added or when t >= 1000000000000. It is not working for me. I am new
to Mathematica. Thanks

x = 2
y = 3
t = 1
w = 0
List1 = {0,1}
f[t_,y_] ==(Floor(Sqrt ((t/4) (y^2-1)^2 + y^2)))^2 - ((t/4) (y^2-1)^2
+ y^2)
While[t<1000000000000,t = t+x;If[f[t,y] = 0, List1 = Append[list1,t];w
= w +1];
If [w = 3,t = 1000000000000, x++]];

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