paper

Chebyshev Polynomials, Sliding Columns, and the -step Fibonacci Numbers

arXiv:2202.12454

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.

5 pages. To appear in Mathematics Magazine, 2022

Chebyshev Polynomials, Sliding Columns, and the $k$-step Fibonacci Numbers · wovepaper