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Journal of Combinatorial Mathematics and Combinatorial Computing

  • Research article

On the Number of Ones in General Binary Pascal Triangles

Heiko Harborth1, Glenn Hurlbert1
1Diskrete Mathematik Department of Mathematics Technische Universitat Braunschweig and Statistics 38023 Braunschweig Arizona State University Germany Tempe, Arizona 85287-1804 USA
  • Published: 31/08/2005

Abstract

This paper answers the question as to whether every natural number \( n \) is realizable as the number of ones in the top portion of rows of a general binary Pascal triangle. Moreover, the minimum number \( \kappa(n) \) of rows is determined so that \( n \) is realizable.

Keywords: Pascal triangle, varied initial values, reduced modulo 2, number of ones.
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Citation
Heiko Harborth, Glenn Hurlbert. On the Number of Ones in General Binary Pascal Triangles[J], Journal of Combinatorial Mathematics and Combinatorial Computing, Volume 054. 99-110. DOI: .