Generalized Leonardo Numbers

  • Yüksel Soykan Department of Mathematics, Art and Science Faculty, Zonguldak Bulent Ecevit University, 67100, Zonguldak, Turkey
Keywords: Leonardo numbers, Leonardo-Lucas numbers, Tribonacci numbers, Fibonacci numbers, Lucas numbers.


In this paper, we investigate the generalized Leonardo sequences and we deal with, in detail, three special cases, namely, modified Leonardo, Leonardo-Lucas and Leonardo sequences. 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 Leonardo, Leonardo-Lucas, Leonardo numbers and Fibonacci, Lucas numbers.


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How to Cite
Soykan, Y. (2021). Generalized Leonardo Numbers. Journal of Progressive Research in Mathematics, 18(4), 58-84. Retrieved from

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