Convolution identities for Tetranacci numbers

Abstract

Convolution identities for various numbers (e.g., Bernoulli, Euler, Genocchi, Catalan, Cauchy and Stirling numbers) have been studied by many authors. Recently, several convolution identities have been studied for Fibonacci and Tribonacci numbers too. In this paper, we give convolution identities with and without binomial (multinomial) coefficients for Tetranacci numbers, and convolution identities with binomial coefficients for Tetranacci and Tetranacci-type numbers.

Infinite series involving Fibonacci numbers and the Riemann zeta function

“…The answer to this questions is "Definitely Yes!". Building on a generating function approach (see also [8,13,14,15,17]) for Fibonacci m-step numbers we will prove many new convolution identities, recovering known results as special cases, including the identities presented above. We note that the generating function approach is not a novel discovery.…”

Tribonacci Numbers and Some Related Interesting Identities

“…T. Komatsu et al [19,20,22], E. Kilic [21] studied the arithmetical properties of Tribonacci numbers and obtained many meaningful convolution identities for T n .…”