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It is possible to find a polynomial of order 5 such that, using that polynomial for the position to term rule, ANY number can be the next number.

However, the only polynomial of degree 4 that will fit the given points is

Un = (15n4 - 214n3 + 1041n2 - 1970n + 1344)/24 for n = 1, 2, ...

Using this rule, the next numbers are 9, 49, 170, ...

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