20170515, 10:13  #1 
"Matthew Anderson"
Dec 2010
Oregon, USA
2^{2}×149 Posts 
find the missing number
Hi MersenneForum,
I was doodling with a spreadsheet program. Can anyone find the missing number in this sequence? 1,4,32,224,1600,?,81152,578048, ... Also, what is the general form that will produce more numbers in the sequence? Best of luck. Regards, Matt There are two arbitrary initial values 
20170515, 12:57  #2  
"Forget I exist"
Jul 2009
Dumbassville
2^{6}·131 Posts 
Quote:


20170515, 15:08  #3 
Aug 2006
3×1,973 Posts 
The missing number is 11392 and the formula is a(n) = 6a(n1) + 8a(n2). That also explains why the number of factors of 2 tends to increase.

20170515, 22:13  #4 
"Matthew Anderson"
Dec 2010
Oregon, USA
2^{2}·149 Posts 
Hi MersenneForum,
Thanks to all the readers and participants. Also, thanks to the Maple command 'rsolve' the expression F(r)=2*F(r1)+4*F(r2) can be expressed as shown in the second attachment. Let me know if a .png file is no good for you. Regards, Matt 
20170515, 22:29  #5 
"Matthew Anderson"
Dec 2010
Oregon, USA
254_{16} Posts 
Hi Mersenneforum,
Some of you may be familiar with the radical expression that goes with the Fibonacci sequence. https://en.wikipedia.org/wiki/Fibona...e_golden_ratio This should be similar. Regards, Matt 
20170515, 22:32  #6 
Aug 2006
3·1,973 Posts 
Yes. The bases of the exponential expression are the roots of the characteristic equation of the recurrence, x^2  6x  8.

20170516, 06:56  #7 
Just call me Henry
"David"
Sep 2007
Cambridge (GMT/BST)
7×19×43 Posts 

20170517, 05:15  #8 
"Harry Willam"
May 2017
USA
2^{2}·5 Posts 
What Number Should Replace the Question Mark?
Option :
A) 9 B) 8 C) 6 D) 0 Tell Me 
20170520, 14:15  #9 
"Matthew Anderson"
Dec 2010
Oregon, USA
2^{2}·149 Posts 
Hi Mersenneforum,
Many thanks to the responses so far. As a learning exercise it would be nice to know the steps between a 'recurrence relation of the first kind' and its 'characteristic equation'. From the Wikipedia article on Lucas Sequence, we see this  Explicit expressions, The characteristic equation of the recurrence relation for Lucas sequences x^2  Px + Q = 0 Must go. Matt 
20170520, 22:13  #10 
Aug 2006
3·1,973 Posts 
The characteristic equation of a recurrence of the form
a(n) = A*a(n1) + B*a(n1) + C*a(n2) + D*a(n3) is x^4  Ax^3  Bx^2  Cx  D and you extend this to lower or higher degree in the obvious way. 
20170521, 01:52  #11 
Sep 2002
Database er0rr
2^{6}×53 Posts 
I am just nitpicking: "x^4  Ax^3  Bx^2  Cx  D" is not an equation. I think you meant "x^4  Ax^3  Bx^2  Cx  D = 0"

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