Fashionable, but unable to tell fact from fiction (testing4l) wrote,
Fashionable, but unable to tell fact from fiction
testing4l

Ask LJ: Finding how a sequence of numbers grows

I have an infinite sequence of numbers which grows superlinearly and I'm attempting to figure out the formula to figure out the next one.

I can prove that it's not a function x^k where k is a natural number <=7 by taking the numbers and figuring out the difference between the numbers in the sequence, then figuring out the differences between those.

The first 10 numbers (and differences) are:
0 80    135    225    375    620    1040    1735    2900    4840    8080
1     55     90    150    245    420     695    1165    1940    3240
2          35    60     95    175     275    470     775    1300
3              25     35    80     100    195     305    525
4                   10    45     20     95     110    220
5                       35    -25     75     15    110
6                          -55     100    -60    95
7                               155   -160    155


It's worth noting the point of inflection on the 4th level. I don't have more than those 10 numbers unfortunately. It's tempting to believe that the next one on the 7th row would be -160 though.

The numbers always end in either 0 or 5, though they don't switch between 0 and 5 in any sort of regular pattern.

That's all I can think of off hand to try and crack that problem.

Incidentally, this is (in theory) part of a class of functions. Those numbers correspond to resource counts for a game (Travian incidentally) and I'm trying to predict how it grows for a program I'm writing.
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