Gregory P. Dresden

activity

20092022

most citedA New Approach to Rational Values of Trigonometric Functions

1 citations · 1 across the 6 of their papers we have counts for

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Showing 2022Show all

3 papers · 1 filter

math.NT2022

Periodic Weighted Sums of Binomial Coefficients

Greg Dresden, Yike Li

Using elementary methods, we establish old and new relations between binomial coefficients, Fibonacci numbers, Lucas numbers, and more.

math.NT2022

On the Brousseau sums $\sum_{i = 1}^{n} i^{p} F_{i}$

Gregory Dresden

We start with new convolution formulas for $F_{n} - n^{p}$ involving only the binomial coefficients. Then, we use those to find direct formulas for the sums $\sum_{i = 1}^{n} i^{p} F_{n - i}$ …

math.NT2022

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

Greg Dresden

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 sum…

Periodic Weighted Sums of Binomial Coefficients

On the Brousseau sums ∑i=1n​ipFi​

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

On the Brousseau sums $\sum_{i = 1}^{n} i^{p} F_{i}$

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