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There are two parts to this puzzle, but I am posting the other part tagged with ‘mathematics’ because it isn’t really a number sequence problem. Part I Find the next number in the sequence: 1,2,3,7,16,65,?

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This is a sequence in OEIS, which makes it rather easy!

https://oeis.org/A000278
0, 1, 1, 2, 3, 7, 16, 65, 321, 4546, 107587
It's a bit like the Fibonacci series, but instead of $a(n) = a(n-1) + a(n-2)$, it's $a(n) = a(n-1) + a(n-2)^2$

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  • $\begingroup$ So did you get it with or without OEIS? $\endgroup$ – Arvasu Kulkarni Feb 3 at 8:24
  • $\begingroup$ With, I'm afraid. I often check as a way to get ideas. It doesn't usually solve it. $\endgroup$ – Dr Xorile Feb 3 at 17:05

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