I need find a closed form for this recurrence relation:

b sub n = b sub n-1 + n^2 for n >0 and b sub 0 = 3

Anybody know how to do this?

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- March 20th 2008, 12:09 AMjzelltsequence formula
I need find a closed form for this recurrence relation:

b sub n = b sub n-1 + n^2 for n >0 and b sub 0 = 3

Anybody know how to do this? - March 20th 2008, 12:28 AMearboth
There is probably a more elegant way than this:

1. Calculate the first five values

2. Calculate the differences between consecutive values

3. Repeat this process until you get a constant sequence.

4. Determine the number of repetitions. That is the degree of the closed form:Code:`degree 3: 3 4 8 17 33 ...`

degree 2: 1 4 9 16 ...

degree 1: 3 5 7 ...

degree 0: 2 2

From the initial row you know:

s_0 = 3

s_1 = 4

s_2 = 8

s_3 = 17

Thus you have to solve a system of simultaneous equations:

After a few steps you'll get: