In a recent video Matt Parker showed a triangular number that also is a square number, 6, and asked if there were more.

A triangular number has the form — shown by Euler — and a square number has the form .

Triangular squares are those numbers for which with .

Examples are (sequence A001109 in OEIS).

To check if triangular numbers are square numbers is easy (code listed below), but a mathematical function would be nicer.

The first thing I tried was to define the triangular number’s square root as a whole number, . This function does not return the square numbers that are triangular but the triangular numbers that are square.

The resulting sequence is (sequence A001108 in OEIS).

```
# Python 2.7.7 Code
# Jonathan Frech 13th of July, 2016
# edited 15th of July, 2016
```