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According to Wittgenstein's Finite Rule Paradox every finite sequence of numbers can be a described in infinitely many ways and so can be continued any of these ways - some simple, some complicated but all equally valid. Conversely, it is possible to find a rule such that any number of your choice can be the next one.

One possible rule, based on a polynomial of order 5, is

Un = (-12*n5 + 205*n4 - 1290*n3 + 3695*n2 - 4638 + 2160)/120 for n = 1, 2, 3, ... and according to that rule, the next three numbers are -10, -104 and -369.

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Q: What are the next three numbers in this pattern 1 2 3 3 6 9?
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