New URL: http://www.iki.fi/~kartturi/matikka/A048757/A048757.htm

On Pascal's Triangle Modulo 2 in Fibonacci Representation.

Antti Karttunen

(Department of Mathematics, University of Helsinki) (*).
E-mail: firstname.surname@iki.fi, http://www.iki.fi/%7Ekartturi


Published in volume 42.1, February 2004 issue of, The Fibonacci Quarterly
(Submitted July 2001 - Third revision June 2002).


Abstract

Inspired by Denton Hewgill's identity:


where

we prove an analogous identity involving the Fibonacci number system:


which holds for all integers n >= 0, d >= 0, where En+d stands for Fn+d (the n+d:th Fibonacci number) if n is even, and Ln+d (the n+d:th Lucas number) if n is odd.


The paper is available on Fibonacci Quarterly's site as a PDF-version of the final published copy and locally (a slightly earlier version) in the following formats:


(* Studying there mathematics at the time of writing).