Let $(R,\mathfrak m)$ be a Noetherian local ring of dimension $d\geq 1.$ Suppose $\lambda(H_{\mathfrak m}^i(R))<\infty$ for some $0\leq i\leq d-1.$

Question Can we say anything about Betti numbers or minimal resolution of $H_{\mathfrak m}^i(R)?$

P.S. Any reference will be extremely helpful.