On some Pascal’s like triangles. Part 3

Krassimir T. Atanassov
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 13, 2007, Number 3, Pages 20–26
Full paper (PDF, 87 Kb)

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Authors and affiliations

Krassimir T. Atanassov
Centre for Biomedical Engineering – Bulgarian Academy of Sciences,
Acad. G. Bonchev Str., Bl. 105, Sofia-1113, Bulgaria

Abstract

In a series of papers, starting with [1, 2], we discuss new types of Pascal’s like triangles. Triangles of the present form, but not with the present sense, are described in different publications, e.g. [3, 5, 6], but at least the author had not found a research with similar idea. In the first part of our research we studied properties of some standard sequences and in the second part – of some “special” sequences. Now, we shall construct (0, 1)-analogous of the Pascal’s like triangles (or “(mod 2)-triangles”) from the both previous papers, i.e., we will construct (mod 2)-values of their elements and will discuss the obtained configurations. We will call the new triangles “(0, 1)-triangles”.

References

1. Atanassov, K., On some Pascal’s like triangles. Part 1. NNTDM, Vol. 13, 2007, No. 1, 31-36.
2. Atanassov, K., On some Pascal’s like triangles. Part 2. NNTDM, Vol. 13, 2007, No. 2, 10-14.
3. Bondarenko, B., Generalized Pascal’s Triangles and Pyramids – Their Fracals, Graphs and Applications, Tashkent, Fan, 1990 (in Russian).
4. Cerin, Z., Sums of squares and products of Jacobsthal numbers. Journal of Integer Sequences, Vol. 10, 2007, Article 07.2.5.
5. Goldwasser, J., W. Klostermeyer, M. mays, G. Trapp, The density of ones in Pascal’s rhombus. Discrete mathematics, Vol. 204, 1999, 231-236.
6. Leyendekkers, J., A. Shannon, J. Rybak. Pattern recognition: Modular Rings & Integer Structure. RaesKvB Monograph No. 9, North Sydney, 2007.
7. Sloane, N.J.A., The On-Line Encyclopedia of Integer Sequences, 2006.