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Re: Function fits with combinations


> 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





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