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September 24th, 2015, 12:07 AM   #11
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Originally Posted by babyjo View Post
Sorry. Can explain more
You can put next $\displaystyle n = 4$ and see, what $\displaystyle L$-terms you need. Then just plug them in and compute. The same applies for $\displaystyle n=5$, etc.
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September 24th, 2015, 03:55 AM   #12
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Is it correct to do in this way?
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.
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September 24th, 2015, 05:18 AM   #13
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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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