fibonacci sequence
public class Numbers {
public static void FibannaciNumbers(int n) {
int x = 0;
int y = 1;
if(n >= 1) {
System.out.print(x + " ");
}
if(n >= 2) {
System.out.print(y);
}
if (n > 2) {
for(int a = n - 2; a > 0; a--) {
int z = y + x;
System.out.print(" " + z);
x = y;
y = z;
}
}
}
}fibonacci sequence
public class Numbers {
public static void FibannaciNumbers(int n) {
int x = 0;
int y = 1;
if(n >= 1) {
System.out.print(x + " ");
}
if(n >= 2) {
System.out.print(y);
}
if (n > 2) {
for(int a = n - 2; a > 0; a--) {
int z = y + x;
System.out.print(" " + z);
x = y;
y = z;
}
}
}
}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;Copyright © 2021 Codeinu
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