Statistical mechanics: Canonical Partition Function for a Polymer in a lattice

First time poster here so I hope I’m not missing anything.

The question

"Consider a simple, lattice model for a polymer. In this model, the polymer sits on a square lattice,
and at every lattice point, the polymer can do one of three things: go straight or choose between
the two directions which makes right $90^{circ}$ angles with respect to its current direction. Each time
the polymer bends (follows a right angle, $90^{circ}$), it pays a bending energy penalty of $epsilon$ ; it pays nothing to continue on straight. Additionally, assume that the starting segment of the polymer is fixed somewhere on the lattice, assume the polymer consists of $N + 1$ segments, and assume that
the polymer is free to overlap itself. Calculate the canonical partition function for the system"

What I’ve tried

The partition function is defined as $Z =sum_{i=0}^infty exp(-beta cdot E_i ) $
The different micro-states in this cases are the different paths of the polymer on the lattice.
So for one micro state, the total energy in the micro state ($E_i$) should be the number of times a $90^{circ}$ turn is made, times the bending energy $epsilon$.
$$
Z = sum_{i=0}^infty exp(-beta cdot epsilon cdot m_i )
$$
where m is the number of times a turn is made.

I am having trouble imagining and finding the combinatorics that describe a path of the polymer along the lattice, where every turn/straight $N$ will be counted. Any hints the right direction would be greatly appreciated!