How can i solve this equation? I am really stuck
$T(n) = T(n + 1) + T(n + 2) + 3n + 1$
$T(0)=2$
$T(1)=3$
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1First you solve the homogeneous version (without the $3n+1$), using the characteristic equation. – The Chaz 2.0 May 09 '13 at 12:43
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1A usual way to do that is to solve the homogeneous part. And then to find a particular solution by the method of undetermnined coefficients. Finally sum these two and determine the constants thanks to the initial conditions. – Julien May 09 '13 at 12:43
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Here is the method. Do not forget to upvote the answers if you benefit from them. – Mhenni Benghorbal May 09 '13 at 12:44
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Another technique. – Mhenni Benghorbal May 09 '13 at 13:23
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@vadim123: Just scroll the page down till you reach the answer you want and then copy the address. – Mhenni Benghorbal May 09 '13 at 13:36
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@MhenniBenghorbal, thanks I was being dense. – vadim123 May 09 '13 at 13:43
1 Answers
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Setting $S_n=T(n)+3n$, you'll obtain $$ S_n=S_{n+1}+S_{n+2}-8. $$
Boris Novikov
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3Just set $F_n=T(n)+3n-8$ immediately and you obtain the Fibonacci recursion. – Raskolnikov May 09 '13 at 12:46
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