On some Pascal’s like triangles. Part 11

Krassimir T. Atanassov
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 21, 2015, Number 3, Pages 45–55
Full paper (PDF, 213 Kb)

Details

Authors and affiliations

Krassimir T. Atanassov
Department of Bioinformatics and Mathematical Modelling
Institute of Biophysics and Biomedical Engineering – Bulgarian Academy of Sciences
Acad. G. Bonchev Str., Bl. 105, Sofia-1113, Bulgaria

Abstract

In a series of papers, Pascal’s like triangles with different forms have been described. Here, new types of triangles is discussed. In the formula for their generation, operation summation is replaced, respectively, by operations multiplication and exponentiation. Some of their properties are studied. The general case is discussed.

Keywords

• Pascal pyramid
• Pascal triangle
• Sequence

AMS Classification

• 11B37

References

1. Atanassov, K. (1985) An arithmetic function and some of its applications. Bull. of Number Theory and Related Topics, 9(1), 18–27.
2. Atanassov, K., On some Pascal’s like triangles. Part 1. Notes on Number Theory and Discrete Mathematics, Vol. 13, 2007, No. 1, 31–36.
3. Atanassov, K., On some Pascal’s like triangles. Part 2. Notes on Number Theory and Discrete Mathematics, Vol. 13, 2007, No. 2, 10–14.
4. Atanassov, K., On some Pascal’s like triangles. Part 4. Notes on Number Theory and Discrete Mathematics, Vol. 13, 2007, No. 4, 11–20.
5. Atanassov, K. (2011) On some Pascal’s like triangles. Part 5. Advanced Studies in Contemporary Mathematics, 21(3), 291–299.
6. Atanassov, K. (2014) On some Pascal’s like triangles. Part 6. Notes on Number Theory and Discrete Mathematics, 20(4), 40–46.
7. Atanassov, K. 2014 On some Pascal’s like triangles. Part 7. Notes on Number Theory and Discrete Mathematics, 20(5), 58–63.
8. Atanassov, K. (2015) On some Pascal’s like triangles. Part 10. Notes on Number Theory and Discrete Mathematics, 21(2), 23–34.