April 11th, 2015, 10:39 PM  #1 
Senior Member Joined: Apr 2013 Posts: 425 Thanks: 24  Recurrence equation
Hello! Solve the recurrence equation $\displaystyle a'_{n}a_{n1}+n^22n=0$. 
April 11th, 2015, 11:58 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,929 Thanks: 2205 
What does $a'_{n}$ mean?

April 12th, 2015, 06:20 AM  #3 
Senior Member Joined: Apr 2013 Posts: 425 Thanks: 24  
April 12th, 2015, 07:04 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,929 Thanks: 2205 
First derivative with respect to what?

April 12th, 2015, 08:16 PM  #5 
Senior Member Joined: Apr 2013 Posts: 425 Thanks: 24  
April 13th, 2015, 05:57 AM  #6 
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 
A priori, f(n) is discrete and has no derivative.

April 13th, 2015, 11:04 AM  #7 
Math Team Joined: Apr 2010 Posts: 2,780 Thanks: 361 
Maybe this definition of a derivate was intended: Arithmetic derivative  OeisWiki 
April 13th, 2015, 07:07 PM  #8 
Global Moderator Joined: Dec 2006 Posts: 20,929 Thanks: 2205 
If $a_n$ has to be a polynomial, $a_n = n^2 + 2n + 3$ and $a'_n = 2n + 2$, the equation is satisfied.

April 13th, 2015, 08:00 PM  #9 
Senior Member Joined: Apr 2013 Posts: 425 Thanks: 24  

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