Submitted:
31 October 2022
Posted:
02 November 2022
You are already at the latest version
Abstract
In this paper, we define and investigate modified p-Leonardo, p-Leonardo-Lucas and p-Leonardo sequences as special cases of the generalized Leonardo sequence. We present Binet's formulas, generating functions, Simson formulas, and the summation formulas for these sequences. Moreover, we give some identities and matrices related with these sequences. Furthermore, we show that there are close relations between modified p-Leonardo, p-Leonardo-Lucas, p-Leonardo numbers and Fibonacci, Lucas numbers.
Keywords:
Leonardo numbers
; Leonardo-Lucas numbers
; p-Leonardo numbers
; p-Leonardo-Lucas numbers
; Tribonacci numbers
; Fibonacci numbers
; Lucas numbers.
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