If we label the first spin as s_1 and the second as s_2 we obtain the following expression for the energy \begin{equation*} E=-Js_1s_2. \end{equation*} The calculation of the energy for the one-dimensional lattice with free ends for one specific spin-configuration can easily be implemented in the following lines
for ( j=1; j < N; j++) {
energy += spin[j]*spin[j+1];
}
where the vector spin[] contains the spin value s_k=\pm 1 .