Help me solve my dumb math question?

[Konrad]

I must be missing something utterly obvious or getting lost in overcomplicated sophistications, but I just can't figure this "simple problem" out.

I've got some numbers:

           Tier3  Tier6  Tier9
Sequence1      6     22     49
Sequence2     18     65    146
Sequence3     28    108    243
Sequence4     70    151    340

I'm supposed to determine the function used so I can calculate values for other Tiers and extend the dataset as far as Tier12 and Sequence5. I think it's possible each Sequence has a different multiplier or slightly modified formula, although I was told (by a dubious source) that all data were derived from the same function.

Complete brain blank. I've tried a thousand approaches, no success. Think I screwed up the FFT, resulting functions didn't reproduce the original data. Got a little lost in the new version of MATLAB, figured I should solve this problem first and relearn the software later. Crazy it may be, but my calculus is pretty sharp while my algebra has rusted away.

I think my most promising approximation has been a summation + exponent approach ... something like f(x)=(x*(x+1)/2)+(t^2), where x = sum of tier values (T3=1+2+3, T6=T3+4+5+6, etc) and t = an arbitrary tier factor (0,1,2).

My formula is flawed, wrong, and fugly, but bad math is the best I could do for now.

Thanx in advance for anyone who tries, lol.

[Xpirate]

I used an on-line vector calculator to get this:

You have entered the following vectors.

v1 = ( 6 , 22 , 49 )
v2 = ( 18 , 65 , 146 )
v3 = ( 28 , 108 , 243 )
v4 = ( 70 , 151 , 340 )

Result of the requested computation.

The vectors v1,v2,v3,v4 are linearly dependent, with the following relation(s) of linear dependence:

16 v1 + (-31) v2 + 14 v3 + v4 = 0

I'm sorry that I can't provide anything else but that.

[Konrad]

Could you linky this online calculator? I'm a little unclear how it approached the data as vector sets.

[Xpirate]

Sorry dude, I did not help at all. You need to know f(1,3)=6, f(2,3)=18 and solve for f, so you can do f(5,12)=? I have forgotten way too much of the math I was supposed to learn.

[Xpirate]

Used this one: http://wims.unice.fr/wims/en_tool~linear~matrix.html