Let $m(G,k)$ and $n(G,k)$ be the number of distinct $k$-element sets of independent edges and vertices, respectively, of a graph $G$. Let $h,p_1,p_2,\ldots,p_h$ be positive integers. For each selection of $h,p_1,p_2,\ldots,p_h$ we construct two graphs $N=N_h(p_1,p_2,\ldots,p_h)$ and $M=M_h(p_1,p_2,\ldots,p_h)$, such that $m(N,k)=m(M,k)$ and $n(N,k)=n(M,k)$ for all but one value of $k$. The graphs $N$ and $M$ correspond respectively to a normal and a Möbius-type belt.