Given ANY number, it is easy to find a polynomial of order 4 that will generate the above four numbers and the selected fifth.
The simplest polynomial or order 3 that will generate the above numbers is
Un = (-53n3 + 399n2 - 880n + 552)/6 for n = 1, 2, 3, ... and accordingly, the next number is -83.
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The next number in the pattern is 324. Each number in the pattern is obtained by multiplying the previous number by 3.
The pattern alternates between two sequences: one decreasing by 1 (18, 13) and the other decreasing by 2 (4, 6). Following this pattern, the next number after 6 should be 3 (6 - 3), and the next number after 13 should be 12 (13 - 1). Thus, the next two numbers in the sequence are 12 and 3.
The next is 3.
It is 43 because 31+12 = 43
It is 15 followed by 6 then 18