Triangular square number

A triangular square number is a number which is both a triangular number and a perfect square. There is an infinity of triangular squares, given by the formula

The k^th triangular square N_k is equal to the s^th perfect square and the t^th triangular number, such that

,

t is given by the formula

.

As k becomes larger, the ratio t/s approaches the square root of two: