Re: Whats with this sequence?
Danny wrote:
This sequence is the difference of each triangle
number and the corresponding Fibonacci number.
e.g.
Starting with the first triangle number and the first
Fibonacci f(1) number --
t---f = difference
1 - 1 =0
3 - 1 =2
6 - 2 =4
10- 3 =7
15- 5 =10
etc.
Gives this resulting sequence --
0,2,4,7,10,13,15,15,11,0,-23,-66,-142,-272,
-490,-851,-1444,-2413,...
Note: the 10th term (0) which is 55-55 = t(10)-f(10)= 0.
All fine and good but,why on the third delta row
beneath this sequence the Fibonacci sequence appears?
Except for the leading 1,1 the 3rd delta sequence is
the Fibonacci sequence excluding the double entry of[1,1]
at the beginning the following starts after the [1,1]--
0,1,1,2,3,5,8,13,21,34,55,89,144...
It just seems strange that this sequence would produce
the Fibonacci sequence in one of its deltas!
Also why did it not list the triangle numbers instead
on say the same or some other delta row?
You could have worked this out. The 3rd deltas are the
Fibonacci numbers because they are the deltas of your
initial sequence of (triangles minus Fibonaccis), which
are the (deltas of triangles) minus (deltas of Fibonaccis).
Now the 3rd deltas of triangles are zero, and the deltas
of Fibonaccis are Fibonaccis all over again, so what you
spotted was not strange at all, it was inevitable.
--
.
Relevant Pages
- Re: c language
... this sequence was described by the Indian mathematicians Gopala and Hemachandra in 1150, who were investigating the possible ways of exactly bin packing items of length 1 and 2. ... In the West, it was first studied by Leonardo of Pisa, who was also known as Fibonacci, to describe the growth of an idealised rabbit population. ... Every positive integer can be written in a unique way as the sum of one or more distinct Fibonacci numbers in such a way that the sum does not include any two consecutive Fibonacci numbers. ... For example, the solutions to reaction-diffusion differential equations can show such a patterning; in biology, genes often express themselves through gene regulatory networks, that is, in terms of several enzymes controlling a reaction, which can be modelled with reaction-diffusion equations. ...
(comp.programming) - Re: Whats with this sequence?
... number and the corresponding Fibonacci number. ... Starting with the first triangle number and the first ... Gives this resulting sequence -- ... difference table is all zeroes from its 3rd row onward. ...
(sci.math) - ++var VS var++
... that ++var is faster than var++ as it just adds one and returns the value, ... The above code generates 17 seconds if the compiler is using optimising and ... As I previously said, I was experimenting with the fibonacci sequence, so I ...
(alt.comp.lang.learn.c-cpp) - Re: 1/89 and the Fibonacci sequence-
... You will see the Fibonacci numbers being generated when you develop the power series, and you will see them to fall into place when you multiply out the identity ... All power series developments of reciprocals of polynomials yield recurrent relations for the coefficients. ... >>Then adding the Fibonacci sequence in this manner -- ... >>Will this continue repeating the period of 1/89>no matter how many fibonacci numbers are added>in this manner? ...
(sci.math) - Re: Fibonacci program
... spartacus wrote: ... i have to program a cobol program where the prompt lists the fibonacci ... number sequence with a maximum of 9 digits. ... So you are a newbie at school and your prof/teacher throws a zinger at you and you really don't know which way is up - 'Fibonacci', 'Compute', 'On Size Error' ..... ...
(comp.lang.cobol) |
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