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 Feb2 awarded Nice Question Jul2 awarded Curious Jan26 awarded Notable Question Nov21 awarded Popular Question Sep15 awarded Self-Learner Aug16 awarded Popular Question Mar1 awarded Yearling Mar1 accepted Generating functions for sum of powers of two Mar1 comment Generating functions for sum of powers of two I flipped a negative sign in the denominator. It is fixed now. Thanks so much for your help! Mar1 revised Generating functions for sum of powers of two added 7 characters in body Mar1 comment Generating functions for sum of powers of two I must have made some mistake. I believe the answer should be $a_n = 2^{n+1} - 2$. Mar1 comment Generating functions for sum of powers of two I have $A(x) = \frac{1}{2x - 1} - \frac{4}{x - 1} - 3$. So I can write it as $A(x) = -3 + \sum (4 - 2^n) x^n$. This is actually the first problem in generating functions I'm doing on my own. I'm not sure where to go from here. Mar1 comment Generating functions for sum of powers of two @wj32 -- I'm trying to learn independently. I'm currently following along in the Analytic Combinatorics class on Coursera, but this is a sequence that I ran into on my own. (Incidentally, this sequence is the expected number of coin flips you need before you get $n$ heads in a row.) Mar1 comment Generating functions for sum of powers of two Thanks @wj32. Where do I go from here? Mar1 revised Generating functions for sum of powers of two added 259 characters in body Mar1 asked Generating functions for sum of powers of two Feb19 awarded Popular Question Jan15 awarded Nice Question Jan1 accepted Sangaku: Show line segment is perpendicular to diameter of container circle Dec28 accepted Expected smallest prime factor