looking for equation to a specific spiral incrementing by a specific rate

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what would be the equation to a spiral which increments by the sum of the previous increment and the increment?

thus the turn gaps would be 0.1 0.2 0.4 0.8 1.6 3.2 6.5 13 26 52 104

what I have is r = 0.3 * theta^2 -1 + 30 * theta

but it doesent seem precisely what I am looking for