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Given any number it is easy to find a rule based on a polynomial of order 7 such that the first seven numbers are as listed in the question and the eighth is the given number. That is, it is easy to find a rule so that any number can be the "next" in the sequence.

The polynomial of order six that fits is

Un = (n6 - 15n5 + 115n4 - 405n3 + 964n2 - 660n + 240)/240 and

accordingly, U8 = 379.

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