|Journal of Integer Sequences, Vol. 15 (2012), Article 12.3.5|
As a consequence of our main result we obtain a generalization of theorem of the product of two determinants.
We show the upper Hessenberg determinants, with -1 on the subdiagonal, belong to our class. Using such determinants allow us to represent terms of various recurrence sequences in the form of determinants. We illustrate this with several examples. In particular, we state a few determinants, each of which equals a Fibonacci number.
Also, several relationships among terms of sequences defined by the same recurrence equation are derived.
(Concerned with sequences
Received December 20 2011; revised version received March 13 2012. Published in Journal of Integer Sequences, March 13 2012.