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Jul 27, 2020 at 16:13 comment added Shawnak Deb Thanks @SubhasishMukherjee! I'll edit my answer to add in the consolidated solution, and I totally agree that the other forms are interesting in their own right.
Jul 27, 2020 at 16:12 history edited Shawnak Deb CC BY-SA 4.0
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Jul 25, 2020 at 12:34 comment added Subhasish Mukherjee Hey Shawnak! Thanks so much for this wonderfully written solution. What you wrote can be consolidated as $f_n = 2^{n-3}+2^{\lceil n/2\rceil - 1}+1$, but I think separating them out leads to more interesting conclusions as you noted. It's a mostly intellectual question that sprung from origami folding, which makes it all the more intriguing.
Jul 25, 2020 at 12:14 vote accept Subhasish Mukherjee
Jul 25, 2020 at 10:52 history edited Shawnak Deb CC BY-SA 4.0
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Jul 25, 2020 at 10:40 history edited Shawnak Deb CC BY-SA 4.0
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Jul 25, 2020 at 10:29 history edited Shawnak Deb CC BY-SA 4.0
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Jul 25, 2020 at 7:56 review First posts
Jul 25, 2020 at 12:37
Jul 25, 2020 at 7:51 history answered Shawnak Deb CC BY-SA 4.0