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 Apr 28 awarded Nice Question Jun 14 awarded Notable Question Feb 2 awarded Nice Question Jul 2 awarded Curious Jan 26 awarded Notable Question Nov 21 awarded Popular Question Sep 15 awarded Self-Learner Aug 16 awarded Popular Question Mar 1 awarded Yearling Mar 1 accepted Generating functions for sum of powers of two Mar 1 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! Mar 1 revised Generating functions for sum of powers of two added 7 characters in body Mar 1 comment Generating functions for sum of powers of two I must have made some mistake. I believe the answer should be $a_n = 2^{n+1} - 2$. Mar 1 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. Mar 1 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.) Mar 1 comment Generating functions for sum of powers of two Thanks @wj32. Where do I go from here? Mar 1 revised Generating functions for sum of powers of two added 259 characters in body Mar 1 asked Generating functions for sum of powers of two Feb 19 awarded Popular Question Jan 15 awarded Nice Question