December 29th, 2011, 07:39 AM  #1 
Newbie Joined: Nov 2011 Posts: 20 Thanks: 0  confusing
I have series: 0,1,0,1,0,1,... For example I have to get fourth number in the series, but with generating function. The generating function is: 0+1x + 0x^2 + 1x^3 + 0x^4+... =(1+x^2 + x^3 + x^4...)(1 + x^2 + x^4 +...)=1/(1x)  1/(1x^2) The formula for getting nth number in the series is given by formula: f(n)= (f^(n) (0))/n! , where f(x) must be n times derivatived, and then x=0 I did that: (1/(1x)  1/(1x^2))''''=(24 x (5+10 x^2+x^4))/(1+x^2)^5 ___(wolfram alpha) I put 0 instead x, and I get f(n)=0/n! = 0 but I should get 1. What is the problem, is the formula wrong or something else? *I know there exist a lot of simpler formulas, but if I have series 0,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1... generating function is powerful tool, and I don't have to use floor, ceiling or modulo functions. 
December 29th, 2011, 10:40 AM  #2  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: confusing Quote:
 
December 29th, 2011, 01:15 PM  #3 
Newbie Joined: Nov 2011 Posts: 20 Thanks: 0  Re: confusing
thanks


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