mersenneforum.org A Fib expression with multiplication
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2016-10-31, 23:56   #1
MattcAnderson

"Matthew Anderson"
Dec 2010
Oregon, USA

22×149 Posts
A Fib expression with multiplication

Hi Math and Computer people,

Some of you may be familiar with the standard Fibonacci expression,, definition.

This is a request for comments.

Please let me know if there are errors.

Regards,
Matt
Attached Files
 October 31 2016 Fib.txt (847 Bytes, 144 views) October 31 2016 Fibonacci give 2.txt (393 Bytes, 137 views)

2016-11-01, 00:50   #2
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

26·131 Posts

Quote:
 Originally Posted by MattcAnderson Hi Math and Computer people, Some of you may be familiar with the standard Fibonacci expression,, definition. This is a request for comments. Please let me know if there are errors. Regards, Matt
the only logical error is you said it didn't have a start but then by naming the coefficient starting within the sequence itself you gave it a start at the second 1 in the sequence of 0,1,1,2,3,5,8 ... it's an example of a lucas sequence ( not to be confused with the lucas numbers). edit: doh and one part you say 1 1 2 3 8 instead of 1 2 3 5 8

Last fiddled with by science_man_88 on 2016-11-01 at 01:17

 2016-11-01, 01:41 #3 MattcAnderson     "Matthew Anderson" Dec 2010 Oregon, USA 22×149 Posts Hi again, Thank you ScienceMan88. You make a good point. There is definitely a difference between the Fibonacci sequence and the Lucas sequence. Regards, Matt
2016-11-01, 02:02   #4
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

100000110000002 Posts

Quote:
 Originally Posted by MattcAnderson Hi again, Thank you ScienceMan88. You make a good point. There is definitely a difference between the Fibonacci sequence and the Lucas sequence. Regards, Matt
terminology counts a lot in sciences as this forum proves again and again you'll find lucas numbers is the correct term the fibonacci numbers technically are a lucas sequence

Last fiddled with by science_man_88 on 2016-11-01 at 02:13

2016-11-01, 07:30   #5
R. Gerbicz

"Robert Gerbicz"
Oct 2005
Hungary

57116 Posts

Quote:
 Originally Posted by MattcAnderson This is a request for comments.
Probably this is an 800 years old formula. See https://en.wikipedia.org/wiki/Fibonacci_number at "Matrix form" section, with different letters:
F(m)*F(n)+F(m-1)*F(n-1)=F(m+n-1).

 2016-11-01, 08:16 #6 MattcAnderson     "Matthew Anderson" Dec 2010 Oregon, USA 22×149 Posts Hi Math and computer people,, Thank you Mr. R. Gerbicz for your comment. Assuming that F(n) = F(n-1) + F(n-2) implies that From the Wikipedia article about Fibonacci numbers https://en.wikipedia.org/wiki/Fibonacci_number I quote - F(m)*F(n) + F(m-1)*F(n-1) = F(m+n-1), F(m)*F(n+1) + F(m-1)*F(n) = F(m+n) In particular, with m=n we infer that F(2n-1) = F(n)^2 + F(n-1)^2 and F(2*n) = [F(n-1) + F(n+1)]*F(n). This expression is available in the literature. At least it is less than 1000 years old. *sigh* Regards, Matt

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