Betti numbers of the conormal module of licci rings

We establish lower bounds for the Betti numbers of the conormal module for licci ideals in a regular local ring. In particular, for a licci Gorenstein ideal I, the i-th Betti number of I/I $$I/I^{2}$$ is at least $$5f_{2i-1}$$ , for $$i\ge 1$$ , where $$f_{n}$$ is the n-th Fibonacci number.