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Stupid Math Puzzle


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I'm pretty good at math but I've always been terrible at these kinds of puzzles.

http://www.smbc-comics.com/comic/puzzle-time

The puzzle doesn't actually have a defined solution; the comic author is just being a jerk. But I wondered if anyone could come up with an actual pattern that would generate this sequence.

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You can interpolate a n-th order polynomial for any set of n+1 points: the curve will pass exactly in every points, but the variations in between may not reflect what you want. So you could find a 7th order polynomial such that f(1) = 0, f(2) = 1, f(3) = 4, f(4) = -13 and so on.

If you don't want random oscillations between you defined points or a curve that is not a polynomial, you can use splines, which are lower-order polynomials patched together to form a smooth curve.

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The nth term can be found with (521/560)n7 - (2587/90)n6 + (43291/120)n5 - (170393/72)n4 + (2085781/240)n3 - (6369907/360)n2 + (638962/35)n - 7219, assuming I haven't screwed up and forgotten to carry a two someplace. :)

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