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Given any number it is possible to find a polynomial of order 5 such that it is a position-to-term rule for the above five and the additional number.

The simplest polynomial of order 4 gives

Un = (n4 - 6n3 + 23n2 - 6n)/12 for n = 1, 2, 3, ...

and accordingly, the next number is 66.

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11y ago

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