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Given any number it is easy to find a rule based on a polynomial of order 6 such that the first six numbers are as listed in the question and the next is the given number. There are also non-polynomial solutions.

However, the only solution based on a polynomial of order 5 is

Un = (11n5 - 195n4 + 1305n3 - 4065n2 + 5704n - 2340)/60 for n = 1, 2, 3, ...

and according to this rule, the next (missing) number is 45.

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