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[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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