Recursion Formulas for the number of $(n, m, k)$-resilient and correlation-immune Boolean mappings

For linear combinations of coordinate functions of mapping from the vectorspace $V_n$ of all binary vectors of length $n$ to the vectorspace $V_m$, recursive formulas for the distribution of weights of some their subfunctions $w_I^J$ and for the distribution of subsets of their spectral coefficients $\Delta_I^J$ are obtained. By mean of these formulas, we obtain the recursive formula for the number of correlation-immune of order $k$ mappings
and the recursive formula for the number of $(n,m,k)$-resilient Boolean mappings.