Generalized Fibonacci Numbers: Sum Formulas of the Squares of Terms


  • Yüksel Soykan Zonguldak Bülent Ecevit University, 67100, Zonguldak, Turkey


Fibonacci numbers, Lucas numbers, Pell numbers, Jacobsthal numbers, sum formulas


In this paper, closed forms of the sum formulas nk=1kWk2 and nk=1kW2−k for the squares of generalized Fibonacci numbers are presented. As special cases, we give summation formulas of Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal and Jacobsthal-Lucas numbers. We present the proofs to indicate how these formulas, in general, were discovered. Of course, all the listed formulas may be proved by induction, but that method of proof gives no clue about their discovery. Our work generalize second order recurrence relations.


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Author Biography

Yüksel Soykan, Zonguldak Bülent Ecevit University, 67100, Zonguldak, Turkey

Department of Mathematics, Art and Science Faculty


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How to Cite

Yüksel Soykan. (2020). Generalized Fibonacci Numbers: Sum Formulas of the Squares of Terms. MathLAB Journal, 5, 46-62. Retrieved from



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