Gib Z said:Depends what f(n) is. For example if f(n) = 2^n, then yours sequence is still the recurrence relation a_0 =1 , a_n+1 = 2 a_n.
maze said:It's not in Sloane, surprisingly.
A recurrence relation is a mathematical equation that describes a sequence of numbers or values by relating each term to one or more of the previous terms in the sequence. It is often used in computer science and mathematics to model and solve problems that involve repeated or recursive calculations.
Finding a recurrence relation allows us to describe and understand a sequence of values in a concise and general form. This can help us to identify patterns and relationships within the sequence, and use them to make predictions or solve problems more efficiently.
The process of finding a recurrence relation involves identifying a pattern or relationship between the terms in a sequence. This can often be done by looking at the difference between consecutive terms or by examining the factors or operations involved in generating the sequence. Once a pattern is identified, it can be expressed as a mathematical equation or formula.
Some common examples of recurrence relations include the Fibonacci sequence, the factorial sequence, and the Tower of Hanoi problem. These can be expressed in terms of their previous terms or in a recursive form, where the solution to a problem is defined in terms of smaller instances of the same problem.
Recurrence relations are used in a variety of real-world applications, such as in computer algorithms, financial modeling, and population growth analysis. They can also be used to model and solve problems in physics, engineering, and other scientific fields. By finding a recurrence relation, we can better understand and predict the behavior of complex systems and phenomena.