Journal of Integer Sequences, Vol. 13 (2010), Article 10.7.8

Hessenberg Matrices and Integer Sequences

Milan Janjić
Department of Mathematics and Informatics
University of Banja Luka
Republic of Srpska
Bosnia and Herzegovina


We consider a particular case of upper Hessenberg matrices, in which all subdiagonal elements are -1. We investigate three type of matrices related to polynomials, generalized Fibonacci numbers, and special compositions of natural numbers. We give the combinatorial meaning of the coefficients of the characteristic polynomials of these matrices.

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(Concerned with sequences A000045 A000124 A000129 A000217 A001076 A001105 A001628 A001629 A001845 A001872 A004006 A005744 A005893 A006190 A006503 A006504 A006522 A006645 A017281 A023607 A027927 A030267 A052918 A054457 A056220 A057979 A073380 A073381 A077985 A080855 A080856 A080857 A105163 A121555 A152881 A168050.)

Received March 31 2010; revised version received July 14 2010. Published in Journal of Integer Sequences, July 16 2010.

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