Formula for finding $n^{th}$ Term of Fibonacci-Like Sequence of Higher Order

Abstract

The Fibonacci and Lucas sequences are well-known examples of second order recurrence sequences. The Fibonacci and Lucas sequences have been discussed in so many articles and books. The well-known Fibonacci sequence $\{F_n\}$ is defined as $F_{n}=F_{n-1}+F_{n-2}$, $n\ge 2$ and $F_{0}=0$, $F_{1} =1$, where $F_{n}$ is a $n^{th}$ number of sequence. Many authors have defined Fibonacci pattern based sequences which are popularized and known as Fibonacci-Like sequences. These are similar to Fibonacci sequences in pattern, but initial conditions are different. In this paper, we present formula for finding $n^{th}$ term of Fibonacci-Like Sequence of Higher Order.