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Old 2004-04-06, 12:15   #1
jinydu
 
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Dec 2003
Hopefully Near M48

2·3·293 Posts
Default Recurrence Equation

c(n+2) = -8c(n+1) - 16c(n), c(1) = -1, c(2) = 8

Given the above recurrence equation and starting conditions, the goal is to find the solution (that is, an equation that calculates c(n) without reference to previous terms).

The characteristic polynomial is:

n^2 = -8n - 16

n^2 + 8n + 16 = 0

n = -4 (repeated root)

What has made this problem difficult for me is the repeated root. Because of the repeated root, the solution given at

http://mathworld.wolfram.com/LinearR...eEquation.html

doesn't work because it involves dividing by zero.

In case it helps, here are some more terms:

c(0) = 0
c(1) = -1
c(2) = 8
c(3) = -48
c(4) = 256
c(5) = -1280
c(6) = 6144
c(7) = -28672

Also, the ratio between successive terms appears to be approaching some number close to -4.

Thanks
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