Is there a formula for the sum $s(n)=\sum_{k=1}^n2^{k^2}$? I know that $\sum^n2^k=2(2^n-1)$ but I dont know if I can use that. If not, is there a big-O upper bound?
Formula for $\sum2^{k^2}$
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summation
closed-form
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0The sequence $2,18,530,66066$ is not even in OEIS. I think that the simplest way to compute $s(n)$ is the obvious one. – 2017-02-26
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0$\sum_{k=0}^n 2^k = 2^{n+1}-1$ is quite obvious when you write it in base $2$, and there is no such formula for $\sum_{k=0}^n 2^{k^2}$ – 2017-02-26
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0@ajotatxe and what would be the obvious one? Something like Euler-Mclaurin or really just adding up? – 2017-02-26
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2An upper bound would be the last term, $O(2^{n^2})$. – 2017-02-26
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0S(n) is almost $2^{n^2}$. – 2017-02-26