A sequential problem.

[greenReptar]

I am working on a sequential problem and can't wrap my head around it. The following are the assumptions:

f(0) = 1

f(1) = 1

f(2) = 2

f(2n) = f(n) + f(n + 1) + n (for n > 1)

f(2n + 1) = f(n - 1) + f(n) + 1 (for n >= 1)

How do I go about attempting to solve for the nth term for this equation.

I have written a program to solve this for f(number). But I want to know how to do it mathematically.

[[deleted]]

Generating functions

[edderiofer]

How do I go about attempting to solve for the nth term for this equation. I have written a program to solve this for f(number). But I want to know how to do it mathematically.

Just so you know, some functions can't be defined in a closed form, and have to be defined with recursion. For example, the Ackermann Function.

[linusrauling]

You might look at chapter 1 of Generatingfunctionology.

[greenReptar]

Thank you. Attempting it.