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566.

This number is obtained by using the position to value rule:

Un = (22n3 - 83n2 + 97n - 28)/2 for n = 1, 2, 3, ...

It is always possible to find a quartic (power 4) polynomial which will generate the above four numbers and then give you any number of your choice as the next number.

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Q: What number comes next in the sequence 4 5 55 220?
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