Summing Formulas For Generalized Tribonacci Numbers

Incomplete generalized Tribonacci polynomials and numbers

The main object of this paper is to present a systematic investigation of a new class of polynomials – incomplete generalized Tribonacci polynomials and a class of numbers associated with the familiar Tribonacci polynomials. The various results obtained here for these classes of polynomials and numbers include explicit representations, generating functions, recurrence relations and summation fo...

Determinantal Representations for Generalized Fibonacci and Tribonacci Numbers

the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract Using certain Hessenberg matrices, we provide some determinantal representations of the general terms of second-and third-order linear recurrence sequences with arbitrary initial values. Moreover, we provide explicit formu...

Some summation formulas involving harmonic numbers and generalized harmonic numbers

Several Explicit and Recursive Formulas for the Generalized Motzkin Numbers

In the paper, the authors find two explicit formulas and recover a recursive formula for the generalized Motzkin numbers. Consequently, the authors deduce two explicit formulas and a recursive formula for the Motzkin numbers, the Catalan numbers, and the restricted hexagonal numbers respectively.

Explicit Formulas and Combinatorial Identities for Generalized Stirling Numbers

In this paper, a modified approach to the multiparameter non-central Stirling numbers via differential operators, introduced by El-Desouky, and new explicit formulae of both kinds of these numbers are given. Also, some relations between these numbers and the generalized Hermite and Truesdel polynomials are obtained. Moreover, we investigate some new results for the generalized Stirling-type pai...