On some Pascal’s like triangles. Part 8

Krassimir Atanassov
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 21, 2015, Number 1, Pages 42–50
Full paper (PDF, 159 Kb)

Details

Authors and affiliations

Krassimir 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, three-dimensional analogues of these triangles are given and some of their properties are studied.

Keywords

• Pascal pyramid
• Pascal triangle
• Sequence

AMS Classification

• 11B37

References

1. Atanassov, K. (2007) On some Pascal’s like triangles. Part 1. Notes on Number Theory and Discrete Mathematics, 13(1), 31–36.
2. Atanassov, K. (2007)On some Pascal’s like triangles. Part 2. Notes on Number Theory and Discrete Mathematics, 13(2), 10–14.
3. Atanassov, K. (2007) On some Pascal’s like triangles. Part 3. Notes on Number Theory and Discrete Mathematics, 13(3), 20-25.
4. Atanassov, K. (2007) On some Pascal’s like triangles. Part 4. Notes on Number Theory and Discrete Mathematics, 13(4), 11–20.
5. Atanassov, K. (2011) On some Pascal’s like triangles. Part 5. Advanced Studies in Contemporary Mathematics, 17(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. Bondarenko, B. (1990) Generalized Pascal’s Triangles and Pyramids – Their Fractals,Graphs and Applications, Tashkent, Fan (in Russian).
9. Cerin, Z. (2007) Sums of squares and products of Jacobsthal numbers. Journal of Integer Sequences, 10, Article 07.2.5.
10. Goldwasser, J., Klostermeyer, W., Mays, M., & Trapp, G. (1999) The density of ones in Pascal’s rhombus. Discrete Mathematics, 204, 231–236.
11. Leyendekkers, J. V., Shannon, A. G., & Rybak, J. (2007) Pattern Recognition: Modular Rings & Integer Structure. Raffles KvB Monograph No. 9, North Sydney.