Prev: proving that Preamble + 9th = (improve the world) and the job of the #25 logic look at USA Constitution
Next: Question about energy eigenvalues of a Hamiltonian, in general
From: emath on 25 Mar 2010 07:56
Hi,
Is there any formulae for sum of squares of fibonacci numbers from 0
to n.
From: emath on 25 Mar 2010 07:57
On 25 Mart, 13:56, emath <emath...(a)gmail.com> wrote:
> Hi,
> Is there any formulae for sum of squares of fibonacci numbers from 0
> to n.

Sorry, my problem is for tribonacci numbers.
From: Dan Cass on 25 Mar 2010 04:06
> Hi,
> Is there any formulae for sum of squares of fibonacci
> numbers from 0
> to n.

Well if f(1)=1 and f(2)=1 and later f(n)=f(n-1)+f(n-2),
as it is usually defined, then one may extend
to f(0)=0 and preserve the recursion.
So summing the squares "from 0th to nth"
is the same as summing from the 1st to nth.
Then f(1)^2 + f(2)^2 + ... + f(n)^2
comes out the same as f(n)*f(n+1).
From: emath on 25 Mar 2010 08:24
On 25 Mart, 14:06, Dan Cass <dc...(a)sjfc.edu> wrote:
> > Hi,
> > Is there any formulae for sum of squares of fibonacci
> > numbers from 0
> > to n.
>
> Well if f(1)=1 and f(2)=1 and later f(n)=f(n-1)+f(n-2),
> as it is usually defined, then one may extend
> to f(0)=0 and preserve the recursion.
> So summing the squares "from 0th to nth"
> is the same as summing from the 1st to nth.
> Then f(1)^2 + f(2)^2 + ... + f(n)^2
> comes out the same as f(n)*f(n+1).

Thank you Dan. But I need a formulae for the sum of squares of
tribonacci numbers from.
Tribonacci sequence is defined as follows:
T_0=0,
T_1=1,
T_2=1,
T_3=2,
T_n=T_{n-1}+T_{n-2}+T_{n-3} for n\geq 4.
From: Dan Cass on 25 Mar 2010 04:27
> On 25 Mart, 13:56, emath <emath...(a)gmail.com> wrote:
> > Hi,
> > Is there any formulae for sum of squares of
> fibonacci numbers from 0
> > to n.
>
> Sorry, my problem is for tribonacci numbers.

Could you give the definition of the tribonacci numbers?
I would guess that some initial values for t(1) t(2) t(3)
are given, and then t(n) = t(n-1) + t(n-2) + t(n-3)
for later n?
 |  Next  |  Last
Pages: 1 2 3
Prev: proving that Preamble + 9th = (improve the world) and the job of the #25 logic look at USA Constitution
Next: Question about energy eigenvalues of a Hamiltonian, in general