  In this study, we present a new generalization of circulant matrices for the
generalized $k$-Horadam numbers, by considering the $g$-circulant matrix
$C_{n,g}(H)=g -circ(H_{k,1},H_{k,2},\ldots ,H_{k,n})$. Also, we calculate the
spectral norm, determinant and inverse of $C_{n,g}(H)$ in such matrices having
the elements of all second order sequences.
