Abstract. We study higher-dimensional interlacing Fibonacci sequences, generated via both Chebyshev type functions and m-dimensional recurrence relations. For each integer m, there exist both rational ...

Description: The binomial transform is a transformation that takes a sequence as an input and gives another sequence as an output according to a certain rule. As an example, we have that the binomial ...

Have you ever heard of the Fibonacci sequence? Or the Golden Ratio? Or the Golden Spiral? These mysterious numbers and shapes are all connected to each other. If you look closely, they can be found in ...

Sequences of numbers have long fascinated both amateur and professional mathematicians. Many people are familiar with the Fibonacci sequence, in which each new term is the sum of the previous two ...

You will need to be confident with arithmetic sequences and the 𝑛th term rule to understand these other types of sequences. A geometric sequence contains numbers that are multiplied by a certain ...

In a book completed in the year 1202, mathematician Leonardo of Pisa (also known as Fibonacci) posed the following problem: How many pairs of rabbits will be produced in a year, beginning with a ...