Journal of Integer Sequences, Vol. 15 (2012), Article 12.3.5 |

Department of Mathematics and Informatics

University of Banja Luka

Republic of Srpska

Bosnia and Herzegovina

**Abstract:**

We examine relationships between two minors of order *n* of some
matrices of *n* rows and *n* + *r* columns. This is done through a
class of determinants, here called *n*-determinants,
the investigation of which is our objective.

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 A000045 A000073 A000108 A000110 A000142 A000166 A000930 A000931 A001519 A001590 A001906 A003659 A057597 A077962 A143805)

Received December 20 2011;
revised version received March 13 2012.
Published in *Journal of Integer Sequences*, March 13 2012.

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