How can I get a function relation with these two sets?

[zeion]

Homework Statement

I have these two sets:

Pairwise, (1, 1) (2, 4) (3, 9) (4, 16). Clearly this is just squared.

How can I get a function relation with like:
(1, 1) (2, 3) (3, 9) (4, 10)

or like

(1, 1) (2, 5) (3, 12) (4, 22)

Homework Equations

The Attempt at a Solution

I know it is exponential...
Can I do something with log?

 

[Dick]

Any number of ways. You could just fit a polynomial to them if you only have four points.

 

[zeion]

Do I need a program to do it or can I do it by algebra..?

 

[Dick]

Sure you can do it by algebra. Write y=x^4+a*x^3+b*x^2+c*x+d. Put in your four x and y values. That gives you a system of four linear equation in a,b,c,d. Solve them. It's certainly easier using a program, but you can do it by hand.

 

[SteveL27]

Do I need a program to do it or can I do it by algebra..?

There's a really cool website for these.

http://oeis.org/

For example if you put in 1,5,12,22 as in your third example you get the Pentagonal numbers, n*(3*n-1)/2.

http://oeis.org/search?q=1+,5+,12+,22&language=english&go=Search

http://en.wikipedia.org/wiki/Pentagonal_number

 

[zeion]

Thanks!