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- Feb 14, 2012

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Let $a_0=2$, $a_1=3$, $a_2=6$, and for $n \ge 3$, $a_n=(n+4)a_{n-1}-4na_{n-2}+(4n-8)a_{n-3}$.

The first few terms are $2,\;\;3,\;\;6,\;\;14, \;\;40, \;\;152, \;\;784, \;\;5168,\;\; 40576, \;\;363392$.

Find with proof a formula for $a_n$ of the form $a_n=c_n+d_n$, where $c_n$ and $d_n$ are well-known sequences.

The first few terms are $2,\;\;3,\;\;6,\;\;14, \;\;40, \;\;152, \;\;784, \;\;5168,\;\; 40576, \;\;363392$.

Find with proof a formula for $a_n$ of the form $a_n=c_n+d_n$, where $c_n$ and $d_n$ are well-known sequences.

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