Given any number it is easy to find a rule based on a polynomial of order 4 such that the first four numbers are as listed in the question and the next is the given number. There are also non-polynomial solutions.
The simplest solution, in the form of a polynomial of order 3 is
Un = (3469n3 - 20661n2 + 37712n - 20346)/6 for n = 1, 2, 3, ... and accordingly, the next number is 14219.
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127.
16 21 22 29
58
47 4+7 = 11 7+11 = 18 11+18=29 18+29=47
-47, -41, -35, -29, -23, -17, -11, -5, 1, etc.