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Mar
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accepted Generating functions for sum of powers of two
Mar
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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
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revised Generating functions for sum of powers of two
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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
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revised Generating functions for sum of powers of two
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asked Generating functions for sum of powers of two
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Jan
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accepted Sangaku: Show line segment is perpendicular to diameter of container circle
Dec
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accepted Expected smallest prime factor