## Closed Form of ...[a][/n] = [3a][/n-1] - [2a][/n-2]

Sequences, counting (including probability), logic and truth tables, algorithms, number theory, set theory, etc.

### Closed Form of ...[a][/n] = [3a][/n-1] - [2a][/n-2]

What is the closed form for recursive equation [a][/0] = 0, [a][/1] = 1 and [a][/n] = [3a][/n-1] - [2a][/n-2]

is the closed form [a][/k+1] = [3a][/k+1-1] - [2a][/k+1-2] ???
hbelle

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Joined: Fri May 28, 2010 1:52 am

hbelle wrote:What is the closed form for recursive equation [a][/0] = 0, [a][/1] = 1 and [a][/n] = [3a][/n-1] - [2a][/n-2]

What is the definition of the square brackets and the "slash" notation?

Thank you!

stapel_eliz

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Joined: Mon Dec 08, 2008 4:22 pm

### Re: Closed Form of ...[a][/n] = [3a][/n-1] - [2a][/n-2]

hbelle wrote:What is the closed form for recursive equation [a][/0] = 0, [a][/1] = 1 and [a][/n] = [3a][/n-1] - [2a][/n-2]

is the closed form [a][/k+1] = [3a][/k+1-1] - [2a][/k+1-2] ???

$a_0 = 0, a_1 = 1 \text{ and } a_n = 3a_{n-1} - 2a_{n-2}$

then the closed form is just

$a_n=2^n-1$

Martingale

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