Determinant Identities for Toeplitz-Hessenberg Matrices with Tribonacci Number Entries [article]

Taras Goy, Mark Shattuck
2020 arXiv   pre-print
In this paper, we evaluate determinants of some families of Toeplitz-Hessenberg matrices having tribonacci number entries. These determinant formulas may also be expressed equivalently as identities that involve sums of products of multinomial coefficients and tribonacci numbers. In particular, we establish a connection between the tribonacci and the Fibonacci and Padovan sequences via Toeplitz-Hessenberg determinants. We then obtain, by combinatorial arguments, extensions of our determinant
more » ... mulas in terms of generalized tribonacci sequences satisfying an r-th order recurrence of a more general form with the appropriate initial conditions, where r>2 is arbitrary.
arXiv:2003.10660v1 fatcat:rqhd33ocmvf6fiedgkjr3sk22q