Chebyshev Polynomials, Sliding Columns, and the $k$-step Fibonacci Numbers
Number Theory
2022-02-28 v1 Combinatorics
Abstract
We give a direct and intuitive proof (via sliding some columns up and down) of the following interesting fact: if we write out the Chebyshev polynomials in a chart and take the sums of coefficients along certain diagonals, we obtain the Fibonaccis, the Tribonaccis, the Tetranaccis, and so on.
Cite
@article{arxiv.2202.12454,
title = {Chebyshev Polynomials, Sliding Columns, and the $k$-step Fibonacci Numbers},
author = {Greg Dresden},
journal= {arXiv preprint arXiv:2202.12454},
year = {2022}
}
Comments
5 pages. To appear in Mathematics Magazine, 2022