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Generalized Compositions and Weighted Fibonacci Numbers
Milan Janjic
In this paper we consider particular generalized compositions of a natural number with a given number of parts. Its number is a weighted polynomial coefficient. The number of all g…
Determinants and Compositions of Natural Numbers
Milan Janjic
We consider a particular type of matrices which belong at the same time to the class of Hessenberg and Toeplitz matrices, and whose determinants are equal to the number of a type o…
On Number of Compositions of Natural Numbers
Milan Janjic
We first give a combinatorial interpretation of coefficients of Chebyshev polynomials, which allows us to connect them with compositions of natural numbers. Then we describe a rela…
Number of Compositions and Convolved Fibonacci numbers
Milan Janjic
We consider two type of upper Hessenberg matrices which determinants are Fibonacci numbers. Calculating sums of principal minors of the fixed order of the first type leads us to co…