I got a particular sequence defined by the following recursive function: $T_n = T_{n-1} \times 2 - T_{n-10}$
I need help converting it to a closed form so I can calculate very large values of n efficiently.
The sequence that I produced this recursive formula from is:
n = 1 to 10: 1,1,2,4,8,16,32,64,128,256
n = 11 to 15: 511,1021,2040,4076,8144
The formula is "quirky" for 1 to 10, but works exactly as stated for all n > 10;