Triangular numbers
From specialfunctionswiki
The triangular numbers $T(n)$ are defined by the formula $$T(n)=\displaystyle\sum_{k=1}^n k.$$ They represent the number of ways to draw an equilateral triangle as in the image below.
Graphical representation of the first six triangular numbers.
Properties
T(n)=n(n+1)/2
T(n+1)=T(n)+n+1
n^2=T(n)+T(n-1)
T(n)^2=T(T(n))+T(T(n-1))
