Special Cases of Generalized Leonardo Numbers : Modified p-Leonardo, p-Leonardo-Lucas and p-Leonardo Numbers

  • Yüksel Soykan Department of Mathematics, Faculty of Science, Zonguldak Bülent Ecevit University, 67100, Zonguldak, Turkey
Keywords: Leonardo numbers, Leonardo-Lucas numbers, p-Leonardo numbers, p-Leonardo-Lucas numbers, Tribonacci numbers, Fibonacci numbers, Lucas numbers


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.


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How to Cite
Soykan, Y. (2022). Special Cases of Generalized Leonardo Numbers : Modified p-Leonardo, p-Leonardo-Lucas and p-Leonardo Numbers. Earthline Journal of Mathematical Sciences, 11(2), 317-342. https://doi.org/10.34198/ejms.11223.317342