The rule of this pattern is obfuscated by the omission of spaces, giving the impression that this is the number "111,359,173,157". However, the underlying pattern follows the function of the Fibonacci series, but adding sets of 3 instead of sets of 2. So, 1+1+1=3, 1+1+3=5, 1+3+5=9, 3+5+9=17, 5+9+17=31, 9+17+31=57.
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+2, +3, +2
x4
The pattern rule is: 4 5 6 7 8 and so the next number will be 33+9 = 42
Multiply by 4
There are many possible answers. One possible rule is: Un = (3n4 - 18n3 + 69n2 - 54n + 120)/8 for n 1, 2, 3, ...