this question is mathematical in its sense and considers the following 1D ising spin model
$$s_1s_2s_3....s_{n-1}$$
where $s_i=\pm 1$.
I would like to find the total number of different configurations after reducing symmetry and 'total magnetization'
for example, for a system of $n=4$ the following terms are symmetric $$(-1,+1,+1,+1),(+1,+1,+1,-1)$$
and the following terms have a the same total magnetization ($\sum s_i =2$) $$(+1,-1,+1,+1),(-1,+1,+1,+1)$$
note that there are only two cases of $\sum s_i=2$ because of the symmetry
with these definitions, can I obtain an analytical expression for the total number of state as a function of $n$?
