/* BC program fibonacci */
"If 1 <= m,n, typing f(m,n) prints the Fibonacci numbers F(i),
i in [m,n]. (Here F(1)=F(2)=1 and 
F(n) = (({1+sqrt(5)}/2)^n-({1-sqrt(5)}/2)^n)/sqrt(5).

Typing l(m,n) prints the Lucas numbers L(i), i in [m,n].
Here L(1)=1, L(2)=3 and L(n) = ({1+sqrt(5)}/2)^n+({1-sqrt(5)}/2)^n.
"
define f(m,n){
auto i,x,y,z,temp
if(m<1||n<1){
   print "m<1 or n<1\n"
   return
}
if (m>n){
  temp=m
  m=n
  n=temp
}
x=0
y=1
if(m==1 && n==1){
  print "F(1)="
  return(1)
}
if(m==1 && n==2){
  print "F(1)=1\n"
  print "F(2)="
  return(1)
}
if(m==1 && n>=3){
      print "F(1)=1\n"
}
i=2
while(i<n){
z=y+x /* z=f(i) */
x=y
y=z
if(i>=m){
   print "F(",i,")=",z,"\n"
}
i=i+1
}
print "F(",i,")="
return(y+x)
}

define l(m,n){
auto i,x,y,z,temp
if(m<1||n<1){
   print "m<1 or n<1\n"
   return
}
if (m>n){
  temp=m
  m=n
  n=temp
}
x=2
y=1
if(m==1 && n==1){
  print "L(1)="
  return(1)
}
if(m==1 && n==2){
  print "L(1)=1\n"
  print "L(2)="
  return(3)
}
if(m==1 && n>=3){
  print "L(1)=1\n"
}
i=2
while(i<n){
z=y+x /* z=l(i) */
x=y
y=z
if(i>=m){
   print "L(",i,")=",z,"\n"
}
i=i+1
}
print "L(",i,")="
return(y+x)
}

/* a(1)=a,a(2)=b,a(n+2)=c*a(n+1)+d*a(n) if n >= 1 */
define r(n,a,b,c,d){
auto x,y,z,i
if (n==1)return(a)
if (n==2)return(b)
x=a;y=b
for(i=3;i<=n;i++){
	z=c*x+d*y
	x=y
	y=z
}
return(z)
}

/* fi(n)=F_n */
define fi(n){
auto a,b,c,i
if (n==1)return(1)
if (n==2)return(1)
a=1;b=1
for(i=3;i<=n;i++){
	c=a+b
	a=b
	b=c
}
return(c)
}

/* lu(n) = L_n */
define lu(n){
auto a,b,c,i
if (n==1)return(1)
if (n==2)return(3)
a=1;b=3
for(i=3;i<=n;i++){
	c=a+b
	a=b
	b=c
}
return(c)
}