Re: Function fits with combinations

*To*: mathgroup at smc.vnet.net*Subject*: [mg122941] Re: Function fits with combinations*From*: Dana DeLouis <dana01 at me.com>*Date*: Thu, 17 Nov 2011 06:05:35 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

> Can anyone help me to either identify the function in question Hi. I may not understand the question correctly, but here's my best guess: Here's my guess for the Function: equ=(1+x+x^2); Example #1: equ^3 //Expand 1+3 x+6 x^2+7 x^3+6 x^4+3 x^5+x^6 CoefficientList[%,x] {1,3,6,7,6,3,1} To Calculate what the 4th item is in the list: Coefficient[equ^3,x,3] 7 Example #2 equ^4 //Expand 1+4 x+10 x^2+16 x^3+19 x^4+16 x^5+10 x^6+4 x^7+x^8 CoefficientList[%,x] {1,4,10,16,19,16,10,4,1} Coefficient[equ^4,x,4] 19 Example #3 equ^5 //Expand 1+5 x+15 x^2+30 x^3+45 x^4+51 x^5+45 x^6+30 x^7+15 x^8+5 x^9+x^10 CoefficientList[%,x] {1,5,15,30,45,51,45,30,15,5,1} = = = = = = = = = = = = = HTH :>) Dana DeLouis On Nov 16, 4:52 am, richardmathur <rickarr... at gmail.com> wrote: > Hello, > I've been attempting to use Wolfram to help me identify a function but > after playing with "fit" it keeps giving me linear/quadratic/etc. > solutions and I am sure that the function generating my data is using > combinations. I have a series of n length/m length pairs and I've been > generating alignments between the two, and in the first segment of the > pair any character can map to 1-3 chars of the latter. The number of > alignments is as follows: > > 3,3 = 1 > 3,4 = 3 > 3,5 = 6 > 3,6 = 7 > 3,7 = 6 > 3,8 = 3 > 3,9 = 1 > > 4,4 = 1 > 4,5 = 4 > 4,6 = 10 > 4,7 = 16 > 4,8 = 19 > 4,9 = 16 > 4,10 = 10 > 4,11 = 4 > 4,12 = 1 > > 5,5 = 1 > 5,6 = 5 > 5,7 = 15 > 5,8 = 30 > 5,9 = 45 > 5,10 = 51 > 5,11 = 45 > 5,12 = 30 > 5,13 = 15 > 5,14 = 5 > 5,15 = 1 > > Can anyone help me to either identify the function in question or > figure out how to point to Wolfram that it almost certainly has to do > with combinations? > > Thanks, > Richard