TY - JOUR
TI - Generalized Fibonacci numbers with five parameters
AU - Tasyurdu Yasemin
JN - Thermal Science
PY - 2022
VL - 26
IS - 102
SP - 495
EP - 505
PT - Article
AB - In this paper, we define five parameters generalization of Fibonacci numbers  that generalizes Fibonacci, Pell, Modified Pell, Jacobsthal, Narayana,  Padovan, k-Fibonacci, k-Pell, Modified k-Pell, k-Jacobsthal numbers and  Fibonacci p-numbers, distance Fibonacci numbers, (2, k)-distance Fibonacci  numbers, generalized (k, r)-Fibonacci numbers in the distance sense by  extending the definition of a distance in the recurrence relation with two  parameters and adding three parameters in the definition of this distance,  simultaneously. Tiling and combinatorial interpretations of generalized  Fibonacci numbers are presented, and explicit formulas that allow us to  calculate the nth number are given. Also generating functions and some  identities for these numbers are obtained.