But I don't know where to fit in n .
if
x1 = 1 then x2+x3+...+xn = k-1 (n-1 x left to choose)
OR
x1 = 2 then x2+x3+...+xn = k-2 (n-1 x left to choose)
The n-1 can be chosen in how many ways? Because the choice for x2 is as you said depending on if x1 = 1 or 2 and also the value of k...
Heh allright! Didn't thought they would be of any interest, since I didn't get any far.
Anyway I have tried to rewrite the the sequence k = x_1 + ... + x_n
in different forms.
only this one I felt was kind of near the solution...
a_i = x _i + i .
Which means I should try to find...
Homework Statement
In how many ways can we create the sum
k = x_1 + x_2 + ... + x_n
where each x_i is either 1 or 2 with repetitions allowed. n <= k <= 2n
For example
n = 4
k = 5
1+1+1+2
1+1+2+1
1+2+1+1
2+1+1+1
are four ways.
Homework Equations
Is this solving...
Ok cool, I solved it!
Now my next problem is to prove F_2n = (F_n-1)^2 + (F_n)^2
So I tried to set r = k in the previous identity but I didn't get a solution.
Here's my attempt
r = k
F_2k = F_k * F_k-2 + F_k+1 * F_k-1
= (F_k-1 + F_k-2) * F_k-2 + F_k+1 * F_k-1
= F_k-1 *...
Homework Statement
Prove for k >= 0, r >= 2
F_(k+r) = F_k * F_(r-2) + F_(k+1) * F_(r-1)
Homework Equations
I wonder if one should use induction ? If so, I don't know how to do it with two variables.
If not, should I use the Fibonacci definition F_n = F_n-1 + F_n-2 in some way by...
Hope this is the right place for this thread.
Homework Statement
Hi I need help with the truth table for a CMOS circuit.
http://www.isk.kth.se/~william/dd/agda/bild/cmos/mos903.gif
Homework Equations
Truth table and
What type of circuit is this? But I guess that's easy to...