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Given any number it is easy to find a rule based on a polynomial of order 5 such that the first five numbers are as listed in the question and the next is the given number. There are also non-polynomial solutions.

The simplest polynomial solution, of order 4, is

Un = (-n4 + 10n3 - 11n2 - 142n + 456)/24 for n = 1, 2, 3, ...

and accordingly, the next in the sequence is U6 = 3.

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Q: What is next in sequence of 13 8 5 4 4?
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