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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;

2 Answers 2