
Differential Equations Ordinary and Partial Differential Equations Math Forum 
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September 24th, 2015, 12:07 AM  #11 
Senior Member Joined: Dec 2013 From: some subspace Posts: 212 Thanks: 72 Math Focus: real analysis, vector analysis, numerical analysis, discrete mathematics  
September 24th, 2015, 03:55 AM  #12 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,640 Thanks: 2624 Math Focus: Mainly analysis and algebra  I can't read that. As to whether you need to calculate the whole sequence: perhaps if you calculate term by term (unless there's a simple pattern); not if you brain the closed form for each term of the sequence  you just put $\displaystyle n = 43$ into the formula.

September 24th, 2015, 05:18 AM  #13 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,932 Thanks: 1127 Math Focus: Elementary mathematics and beyond 
This recurrence relation has complex eigenvalues. After kludging around I found $\displaystyle L_n=\dfrac{1}{10}\left( \left(1+\dfrac{\sqrt2}{2}i\right)^n+\left(1\dfrac{\sqrt2}{2}i \right)^n\right)$ 

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