Hey guys. I was just wondering if you could help me with the following problem from the putnam exam. I've tried subtracting familure sequences from the given one, but none these sequences, once subtracted, yielded a sequence that i'm familure with.

Anyways, here is the problem T(z) means the zth term in the seqeuence

Let T(n)=(n+4)T(n-1)-4nT(n-2)+(4n-8)T(n-3)

The first few terms of this sequence are: 2. 3. 6, 14, 40, 152, 784, 4168...

Show that T(n) can be written in the form A(n)+B(n) where A, B are well known sequences.

Here is a list of sequences that I've tried thus far.

1. Catalan numbers.

2. sum of the nth row of pascal's triangle.

3. triangle numbers

4. 1, 2, 3, 4,5...

5. Powers of 2 starting with 2^0

6. Fibbonacii numbers.

The catalan numbers together with the fibbonacii numbers works for a small number of consecuitive terms, but then breaks down; together with the catalan numbers, the case is the same.

Any ideas would be appreciated.