Generalized John Numbers

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


In this paper, we define and investigate the generalized John sequences and we deal with, in detail, two special cases, namely, John and John-Lucas 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 John and John-Lucas numbers and Pell, Pell-Lucas numbers.


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How to Cite
Soykan, Y. (2022). Generalized John Numbers. Journal of Progressive Research in Mathematics, 19(1), 17-34. Retrieved from