On a homogeneous recurrence relation for the determinants of general pentadiagonal Toeplitz matrices

Pentadiagonal Toeplitz matrices frequently arise in many application areas and have been attracted much attention in recent years. In this paper, we present a numerical algorithm of O(logn)O(logn) for computing the determinants of general pentadiagonal Toeplitz matrices without imposing any restrictive conditions. In addition, we investigate some special pentadiagonal Toeplitz determinants and their relations to well-known number sequences, and give a few identity formulas for the ordinary Fibonacci sequences and the generalized kk-Fibonacci sequences.