N + 1 = \sum\limits_{i = i_0 + 1}^k {\left( \begin{array}{c}
 x_i \\ 
 i \\ 
 \end{array} \right)} + \left( \begin{array}{c}
 x_{i_0 } + 1 \\ 
 i_0 \\ 
 \end{array} \right) + \sum\limits_{i = 1}^{i_0 - 1} {\left( \begin{array}{c}
 i - 1 \\ 
 i \\ 
 \end{array} \right)}