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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 rule is

Un = (n4 - 12n3 + 50n2 - 69n + 36)/6 which gives the next number as 21

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11y ago

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