fibonacci numbers
f(n) = f(n-1) + f(n-2) f(6) ^ /\ f(5) + f(4) ^ /\ /\ f(4) + f(3) f(3) + f(2) ^ ^ ^ ^ /\ /\ /\ /\ f(3) + f(2) f(2) +f(1) f(2) + f(1) f(1) + f(0) ^ ^ ^ ^ /\ /\ /\ /\ f(2) + f(1) f(1) + f(0) f(1)+ f(0) f(1) + f(0) ^ /\ f(1) + f(0) //f(6) = 8 ==> f(1)*8 f(1) appears 8 times double feb = (1/Math.pow(5,0.5)) * (Math.pow((1+Math.pow(5,0.5))/2,n)) - (1/Math.pow(5,0.5))* (Math.pow((1-Math.pow(5,0.5))/2,n)); f(1) == 1;
fibonacci numbers
f(n) = f(n-1) + f(n-2) f(6) ^ /\ f(5) + f(4) ^ /\ /\ f(4) + f(3) f(3) + f(2) ^ ^ ^ ^ /\ /\ /\ /\ f(3) + f(2) f(2) +f(1) f(2) + f(1) f(1) + f(0) ^ ^ ^ ^ /\ /\ /\ /\ f(2) + f(1) f(1) + f(0) f(1)+ f(0) f(1) + f(0) ^ /\ f(1) + f(0) //f(6) = 8 ==> f(1)*8 f(1) appears 8 times double feb = (1/Math.pow(5,0.5)) * (Math.pow((1+Math.pow(5,0.5))/2,n)) - (1/Math.pow(5,0.5))* (Math.pow((1-Math.pow(5,0.5))/2,n)); f(1) == 1;
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