# 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: