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Ars Combinatoria

  • Research article

The Binet Formula for the \(k\)-Generalized Fibonacci Numbers

Sheng-liang Yang1, Hui-ting Zhang1
1Department of Applied Mathematics Lanzhou University of Technology Lanzhou, Gansu, 730050, P.R. China
  • Published: 31/07/2014

Abstract

In this paper, using the generating function, we derive Binet formulas and determinant expressions for the k-generalized Fibonacci numbers and Lucas numbers. As applications, we obtain some new recurrence relations for the Stirling numbers of the second kind and power sums.

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Citation
Sheng-liang Yang, Hui-ting Zhang. The Binet Formula for the \(k\)-Generalized Fibonacci Numbers[J], Ars Combinatoria, Volume 116. 193-204. .