**Volume 28** ▶ Number 1 ▷ Number 2 ▷ Number 3 ▷ Number 4

**Character formulas in terms of R_{β} and R_{m} functions**

*Original research paper. Pages 1—8*

M. P. Chaudhary, Sangeeta Chaudhary and Kamel Mazhouda

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*R*and

_{β}*R*functions. Folsom [6] studied character formulas and Chaudhary [5] expressed those formulas in terms of continued fraction identities. Andrews et al. [2] introduced multivariate

_{m}*R*-functions, which are further classified as

*R*;

_{α}*R*, and

_{β}*R*(for

_{m}*m*= 1, 2, 3, …) functions by Srivastava et al. [10].

**On the Vieta–Jacobsthal-like polynomials**

*Original research paper. Pages 9—19*

Wanna Sriprad, Somnuk Srisawat and Kitsana Charoenchaianan

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**Corrigendum to “On the dimension of an Abelian group” [Notes on Number Theory and Discrete Mathematics, 2022, Volume 27, Number 4, Pages 267—275]**

*Corrigendum. Page 20*

Timo Tossavainen and Pentti Haukkanen

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**Factorials as repdigits in base b**

*Original research paper. Pages 21—25*

Nurettin Irmak and Alain Togbé

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**Multicomponent hybrid numbers: On algebraic properties and matrix representations of hybrid-hyperbolic numbers**

*Original research paper. Pages 26—40*

Bahar Doğan Yazıcı and Murat Tosun

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**The amplitude of Motzkin paths**

*Original research paper. Pages 41—47*

Helmut Prodinger

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**Cycles of higher-order Collatz sequences**

*Original research paper. Pages 48—63*

John L. Simons

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**Determinantal and permanental representations of companion sequences associated to the r-Fibonacci sequence
**

*Original research paper. Pages 64—74*

Hacène Belbachir and Ihab-Eddine Djellas

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*r*-Fibonacci sequence were defined. The aim of this paper is to give some determinantal and permanental representations of these sequences via Hessenberg matrices. Several representations of classical sequences and polynomials are established. We conclude by using our representations to give

*n*consecutive terms of companion sequences simultaneously.

**Two theorems on square numbers**

*Original research paper. Pages 75—80*

Nguyen Xuan Tho

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**Set partitions with isolated successions**

*Original research paper. Pages 81—91*

Toufik Mansour and Augustine O. Munagi

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We also consider a corresponding analog of the associated Stirling numbers of the second kind.

**Sums involving generalized harmonic and Daehee numbers**

*Original research paper. Pages 92—99*

Neşe Ömür and Sibel Koparal

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**Partitions with k sizes from a set**

*Original research paper. Pages 100—108*

A. David Christopher

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**A note on generalized and extended Leonardo sequences**

*Original research paper. Pages 109—114*

Anthony G. Shannon and Ömür Deveci

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**Leonardo’s bivariate and complex polynomials
**

*Original research paper. Pages 115—123*

Milena Carolina dos Santos Mangueira, Renata Passos Machado Vieira, Francisco Regis Vieira Alves and Paula Maria Machado Cruz Catarino

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*x*,

*y*and the imaginary unit

*i*in the sequence of Leonardo. Nevertheless, the mathematical results from this process of complexification of these numbers are studied, correlating the mathematical evolution of that sequence.

**On certain inequalities for the prime counting function – Part II**

*Original research paper. Pages 124—128*

József Sándor

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*π*(

*x*).

**Linear recurrence sequence associated to rays of negatively extended Pascal triangle**

*Original research paper. Pages 129—142*

Hacène Belbachir, Abdelkader Bouyakoub and Fariza Krim

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**On two new combined 3-Fibonacci sequences. Part 3
**

*Original research paper. Pages 143—146*

Krassimir T. Atanassov

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*n*-th members are given.

*This issue of the International Journal “Notes on Number Theory and Discrete Mathematics” is published with the financial support of the Bulgarian National Science Fund, Grant Ref. No. KP-06-NP3/43/2021.*