There are infinitely many possible solutions.
The simplest polynomial, of degree 5 is:
Un = (76n5 - 1285n4 + 8130n3 - 23735n2 + 31334n - 14400)/120 for n = 1, 2, 3, ...
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The pattern is this: The number before, plus itself plus 2. For example: 1 (number)+ 0 (number berfore)+ 2 (always use a two in this pattern) = 3 then 1+3+2=6 then 3+6+2+11 and 6+11+2=19, which is your pattern. So the answer is 11+19+2=32. Now the pattern is 1,3,6,11,19,32 Thats a wrap.
Add the previous 2 numbers to get the next number.
The numbers are what you get when you make a sum of reciprocal exponents. N(1) = 1^1 = 1 N(2) = 1^2 + 2^1 = 1 + 2 = 3 N(3) = 1^3 + 2^2 + 3^1 = 1 + 4 + 3 = 8 N(4) = 1^4 + 2^3 + 3^2 + 4^1 = 1 + 8 + 9 + 4 = 22 The next number in the pattern would be 2780.
first number +3 2nd number +2
It's adding the previous number to the current number, then continuing the pattern. 1 + 1 = 2 1 + 2 = 3 2 + 3 = 5 3 + 5 = 8 5 + 8 = 13 And so forth.