December 21st, 2012, 02:54 PM  #1 
Senior Member Joined: Dec 2012 Posts: 148 Thanks: 0  Fibonacci 
December 21st, 2012, 04:04 PM  #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: Fibonacci
They're both linear recurrences ("Cfinite"); the first is a(n) = 4a(n1) + 3a(n2)  9a(n3) + 2a(n4) + a(n5) and the second is a(n) = 5a(n1)  3a(n2)  a(n3).

December 21st, 2012, 04:48 PM  #3  
Senior Member Joined: Dec 2012 Posts: 148 Thanks: 0  Re: Fibonacci Quote:
 
December 23rd, 2012, 02:22 PM  #4  
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: Fibonacci Quote:
 
December 26th, 2012, 08:48 PM  #5 
Senior Member Joined: Dec 2012 Posts: 148 Thanks: 0  Re: Fibonacci  I solved this... 
December 26th, 2012, 09:30 PM  #6 
Senior Member Joined: Dec 2012 Posts: 148 Thanks: 0  Re: Fibonacci
And also 
December 27th, 2012, 05:20 AM  #7 
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: Fibonacci
You might enjoy the book A = B, in which such identities are called "routine".

December 27th, 2012, 07:32 AM  #9 
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: Fibonacci
What are you calling "useless", your identities or the book?

December 27th, 2012, 07:48 PM  #10  
Senior Member Joined: Dec 2012 Posts: 148 Thanks: 0  Re: Fibonacci Quote:
 

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