I have a sequence defined by the following recursive formula:

$\displaystyle T_n = T_{n-1} \times 2 - T_{n-10}$

This produces the sequence:

n = 1 to 10:1, 1, 2, 4, 8, 16, 32, 64, 128, 256

n = 11 to 15:511, 1021, 2040, 4076, 8144

note: n=1 is an anomaly.

I need help converting the formula to a closed form. The closed formula doesn't have to reproduce the above sequence for the n = 1 to 10 parts if it makes it any easier. I can account for those special cases in my program.