- #1
ramsey2879
- 841
- 3
[tex] C(a,b) = a^2 + ab -b^2[/tex]
The characteristic value of a Fibonacci sequence is an interesting property.
1) C(a,b) = C(a,a-b)
2) C(a,b) * C(c,d) = C(ac+ad-bd,bc-ad)
3) C(a,b) * C(a,a-b) = C(2a^2-2ab+b^2,2ab-b^2) =(C(a,b))^2
[tex]C(a,b)^n = C(A_{n},-B_{n})[/tex]
[tex]A_{n}=\sum_{i=0}^{n}F_{i-1}nCia^{i}b^{(n-i)}[/tex]
[tex]B_{n}=\sum_{i=0}^{n}F_{i-2}nCia^{i}b^{(n-i)}[/tex]
Opps the last two equations are sums as i goes from 0 to n
[tex]F_i[/tex] ={-1,1,0,1,1,2,3...} with [tex]F_{0}= 0[/tex]
nCi are the binominal coefficients
The characteristic value of a Fibonacci sequence is an interesting property.
1) C(a,b) = C(a,a-b)
2) C(a,b) * C(c,d) = C(ac+ad-bd,bc-ad)
3) C(a,b) * C(a,a-b) = C(2a^2-2ab+b^2,2ab-b^2) =(C(a,b))^2
[tex]C(a,b)^n = C(A_{n},-B_{n})[/tex]
[tex]A_{n}=\sum_{i=0}^{n}F_{i-1}nCia^{i}b^{(n-i)}[/tex]
[tex]B_{n}=\sum_{i=0}^{n}F_{i-2}nCia^{i}b^{(n-i)}[/tex]
Opps the last two equations are sums as i goes from 0 to n
[tex]F_i[/tex] ={-1,1,0,1,1,2,3...} with [tex]F_{0}= 0[/tex]
nCi are the binominal coefficients
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