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How can I plot

Plotting the sequence

$$u_n = 2u_{n-1}-u_{n-2}.$$

with starting values $u_0=1$ and $u_1=2$ in Wolframalpha ? Or any graphing calculator.

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Out of curiosity, why do you want to plot it? –  Daniel Fischer Nov 8 '13 at 1:32
    
@DanielFischer visualisation –  user106280 Nov 8 '13 at 1:37
    
Aha. I don't know how to make Wolfram Alpha plot it, but I can tell you that $u_n = n+1$, so you can visualise that even without plot. –  Daniel Fischer Nov 8 '13 at 1:39
    
@DanielFischer But how did you get there? Do you know how to put it on any graphing calculator? –  user106280 Nov 8 '13 at 1:57
    
Do you mean $u_n = 2u_{n-1} + u_{n-2}?$ –  Omnomnomnom Nov 8 '13 at 2:19
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1 Answer

You can find the answer on Wolfram Alpha like this. Alternatively, if you have a graphing calculator, you can find the sequence using the sequence graphing mode, as this tutorial demonstrates.

Recursive definitions like this can be resolved fairly easily using either generating functions or the $Z$-transform.

EDIT: Apparently, my link for WA doesn't work for some people for some reason. When I follow my earlier link, I get the following from WA:

Wolfram Alpha sequence stuff

I don't know why it wouldn't work for anyone.

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"Wolfram|Alpha doesn't know how to interpret your input." says Wolfram|Alpha. –  Lord Soth Nov 8 '13 at 3:28
    
@LordSoth I've added a screenshot of what it shows when I click the link. –  Omnomnomnom Nov 8 '13 at 4:23
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