/sci/ - Science & Math

[Ruby !!iPJbBu5S79g No.6298029]

Hey /sci/, got a bit of a math problem for ya. I've been trying to find out if there is a pattern in the power point progression of psions in the Pathfinder RPG. The function looks like this:

f(1) = 2 f(6) = 35 f(11) = 106 f(16) = 221
f(2) = 6 f(7) = 46 f(12) = 126 f(17) = 250
f(3) = 11 f(8) = 58 f(13) = 147 f(18) = 280
f(4) = 17 f(9) = 72 f(14) = 170 f(19) = 311
f(5) = 25 f(10) = 88 f(15) = 195 f(20) = 343

I have tried checking the derivative and second derivative of this function, and seeing how these values increase over time, and tried seeing if they skip certain primes or something... but every attempt for finding a pattern eludes me. I am curious if it is possible to map this function at all to determine values for n>20, or if this cannot fit something consistent.

Any math folks want to take a shot at finding a pattern to this?

Pic unrelated.

[Anonymous No.6298036]

f(n) - f(n-1) goes
4, 5, 6, 8, 10, 11, 12, 14, 16, 18, 20, 21, 23, 25, 26, 29, 30, 31, 32

>checking the derivative
Needs to be a continuous function.

I'd say the game people started with 4, 5, 6, 7, 8, ... and tweaked it from there.

[Anonymous No.6298041]

excel says the trendline is
x*x*0.8422+x*0.2221+2.2675

[Ruby !!iPJbBu5S79g No.6298072]

>>6298041

Almost. Still gonna have a bit of variance I suppose, but everything's within 0.5 of the right answer.

[Anonymous No.6298096]

http://oeis.org/search?q=2%2C+6%2C11%2C17%2C25%2C35%2C46%2C58%2C72%2C88&sort=&language=english&go=Search