Direct formula derived from recursive formula

[Eider]

Homework Statement

I have a recursive formula and I'm trying to find a direct formula.

Homework Equations

The recursive formula: T(n) = T(n-2) + n^2

No base is given. The question says "Assume that T(n) is constant for n <- 2

The Attempt at a Solution

T(1) = 0
difference: 4
T(2) = 4
difference: 6
T(3) = 10
difference: 8
T(4) = 18
difference: 10
T(5) = 28

So the difference is 2n, but then I get stuck and don't know how to go further and get a direct formula.

 

[ystael]

Do you know the explicit formula for 1 + 2 + \dots + n? It will help you solve this problem, and it's something you should know anyway. (Hint: fold the sequence in the middle.)

 

[Eider]

The sum from k=0 to n of s+kv = (n+1) s + 1/2 n(n+1)v

But I don't know what to do because the difference doesn't start with 2

 

[ystael]

Imagine it did, then correct for the problem afterward!