ON TERMS OF THE SEQUENCE {u(n)}


Kilic N.

ARS COMBINATORIA, cilt.146, ss.243-254, 2019 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 146
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1073/pnas.1819476116
  • Dergi Adı: ARS COMBINATORIA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.243-254
  • İstanbul Üniversitesi-Cerrahpaşa Adresli: Evet

Özet

In this paper, we consider the generalized Fibonacci sequence {u(n)}. We derive a generating matrix for both the sums of squares of the form Sigma(n)(k=0) q(n-k)u(k)(2) (q not equal 0) and the products of the form qu(n)u(n+2) (q not equal 0). Also, we give a matrix method to generate the sums of product of two consecutive terms u(n)n(n+1), as well as the product qu(n)u(n+2) (q not equal 0). Furthermore we obtain generating functions and combinatorial representations of u(n)u(n+1) and u(n-1)u(n+1).