# Tangle

Loops of length 4n on square grid that turn at each step and return to start in original direction, OEIS:A000644.

$\boldsymbol{T}_{+}=\begin{pmatrix}1 & 0 & 0\\0 & i & 0\\0 & 0 & -i\end{pmatrix}\;,\quad \boldsymbol{T}_{-}=\begin{pmatrix}1 & -2i & 2i\\0 & 0 & i\\0 & -i & 0\end{pmatrix}$

## Features

• High performance Tangle count