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On the Number of Ones in General Binary Pascal Triangles

Heiko Harborth1, Glenn Hurlbert2
1Diskrete Mathematik Technische Universitat Braunschweig 38023 Braunschweig Arizona State University Germany
2 Department of Mathematics Technische and Statistics Arizona State University Tempe, Arizona 85287-1804 USA

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 κ(n) of rows is determined so that n is realizable.

Keywords: Pascal triangle, varied initial values, reduced modulo 2, number of ones.