General convolution sums involving Fibonacci m-step numbers
arxiv(2024)
摘要
In this paper, using a generating function approach, we derive several new
convolution sum identities involving Fibonacci m-step numbers. As special
instances of the results derived herein, we will get many new and known results
involving Fibonacci, Tribonacci, Tetranacci and Pentanacci numbers. In
addition, we establish some general results providing insights into the inner
structure of such convolutions. Finally, some mixed convolutions involving
Fibonacci m-step numbers and Jacobsthal and Pell numbers will be stated.
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