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Thread: + = !
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22nd April 2007 15:41 #1
+ = !
F_0:=0 ,F_1:=1 , F_n+2:=F_n + F_n+1
F_m+n = F_m*F_n+1 + F_m-1*Fn
m,n
, m n, m+1 i n+1... , !
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22nd April 2007 15:49 #2
EDIT: .... .
... 
- -> ...
1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13...
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89...
F_(n+m) = F_(m)*F_(n+1) + F_(m-1)*F_(n)
n=4, m=5:
F_(4+5) = F_5*F_5 + F_4*F_4
F(9) = F_(5)*f_(5) + F_(4)*F_(4)
13 = 3*3 + 2*2
EDIT2: .... .
n=n+1, m=m+1:
F_(n+m+2) = F_(m+1)*F_(n+2) + F_(m)*F_(n+1)
F_(4+5+2) = F_(5+1)*F_(4+2) + F_(5)*F_(5)
F_(11) = F_(6)*F_(6) + F_(5)*F_(5)
34 = 5*5 + 3*3 = 25 +9
... ( ) 2 1 4- .
F_(13) = F_(7)*F_(7) + F_(6)*F_(6)
89 = 64 + 25
-----------------------------------Last edited by OCFreeze; 22nd April 2007 at 16:31.
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22nd April 2007 16:33 #3
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22nd April 2007 16:35 #4
( n=0 ):
F[m]=F[m]*F[0+1]+F[m-1]*F[0]=F[m]*1+F[m-1]*0=F[m] !
F[m+1]=F[m]*F[1+1]+F[m-1]*F[1]=F[m]*1+F[m-1]*1=F[m]+F[m-1]=F[m+1] !
, , :
F[m+n]=F[m]*F[n+1]+F[m-1]*F[n]
F[m+n+1]=F[m]*F[n+2]+F[m-1]*F[n+1]
, n=0 ( ) . F[m+n+2] :
F[m+n+2]=F[m+n+1]+F[m+n]=(F[m]*F[n+2]+F[m-1]*F[n+1])+(F[m]*F[n+1]+F[m-1]*F[n])=F[m]*(F[n+2]+F[n+1])+F[m-1]*(F[n+1]+F[n])=F[m]*F[n+3]+F[m-1]*F[n+2]
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22nd April 2007 16:47 #5
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22nd April 2007 16:57 #6




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