# Triangular Squares

2016-07-16, post № 133

**programming**, **Python**, **Wolfram Language**, #equation, #number, #number theory, #numbers, #OEIS, #square, #triangle, #triangles

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).