If n is Triangular then so is 9n + 1

Theorem
Let $n$ be a triangular number.

Then $9 n + 1$ is also triangular.

Proof
Let $n$ be triangular.

Then:
 * $\exists k \in \Z: n = \dfrac {k \paren {k + 1} } 2$

So:

which is triangular.