Betti numbers of modules of essentially monomial type

Let $R$ be a Noetherian local ring. In this paper we supply formulae for computing the ranks of syzygy and Betti numbers of $R$-modules of essentially monomial type. These modules are defined with respect to various $R$-regular sequences. For example, finite length modules of monomial type over regular local rings of dimension $n$ are modules of essentially monomial type with respect to $R$-regular sequences of length $n$. If a module is of essentially monomial type with respect to an $R$-regular sequence of length $n$, then the rank of its $i$-th syzygy is at least $\binom {n-1}{i-1}$ and its $i$-th Betti number is at least $\binom ni$.