Consider the equation

Here are the first few solutions:

y = 0, y = 6

y = 6, y = 210

y = 210, y = 7140

y = 7140, y = 242556

y = 242556, y = 8239770

y = 8239770, y = 279909630

y = 279909630, y = 9508687656

y = 9508687656, y = 323015470680

y = 323015470680, y = 10973017315470

y = 10973017315470, y = 372759573255306

y = 372759573255306, y = 12662852473364940

y = 12662852473364940, y = 430164224521152660

y = 430164224521152660, y = 14612920781245825506

y = 14612920781245825506, y = 496409142337836914550

y = 496409142337836914550, y = 16863297918705209269200

is a square

Using the square roots:

…………………. n = 14

……………….. n = 84

……………… n = 492

……………. n = 2870

……………. n = 16730

………….. n = 97512

………… n = 568344

………. n = 3312554

………. n = 19306982

…….. n = 112529340

…… n = 655869060

…. n = 3822685022

…. n = 22280241074

… n = 129858761424