Matrix Powers of Column-Justified Pascal Triangles and Fibonacci Sequences
Combinatorics
2007-05-23 v1 Number Theory
Abstract
If L, respectively R are matrices with entries binom{i-1,j-1}, respectively binom{i-1,n-j}, it is known that L^2 = I (mod 2), respectively R^3 = I (mod 2), where I is the identity matrix of dimension n > 1 (see P10735-May 1999 issue of the American Mathematical Monthly). We generalize it for any prime p, and give a beautiful connection to Fibonacci numbers.
Cite
@article{arxiv.math/0010186,
title = {Matrix Powers of Column-Justified Pascal Triangles and Fibonacci Sequences},
author = {Rhodes Peele and Pantelimon Stanica},
journal= {arXiv preprint arXiv:math/0010186},
year = {2007}
}
Comments
13 pages