Python 3.10.7 (main, Jan  1 1970, 00:00:01) [GCC 11.3.0]
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IPython 8.5.0 -- An enhanced Interactive Python. Type '?' for help.

In [1]: recor([1,1],[0,1],100)
0 -> 0	
1 -> 1	
2 -> 1	[1.0]
3 -> 2	[2.0]
4 -> 3	[1.5]
5 -> 5	[1.6666666666666667]
6 -> 8	[1.6]
7 -> 13	[1.625]
8 -> 21	[1.6153846153846154]
9 -> 34	[1.619047619047619]
10 -> 55	[1.6176470588235294]
11 -> 89	[1.6181818181818182]
12 -> 144	[1.6179775280898876]
13 -> 233	[1.6180555555555556]
14 -> 377	[1.6180257510729614]
15 -> 610	[1.6180371352785146]
16 -> 987	[1.618032786885246]
17 -> 1597	[1.618034447821682]
18 -> 2584	[1.6180338134001253]
19 -> 4181	[1.618034055727554]
20 -> 6765	[1.6180339631667064]
21 -> 10946	[1.6180339985218033]
22 -> 17711	[1.618033985017358]
23 -> 28657	[1.6180339901755971]
24 -> 46368	[1.618033988205325]
25 -> 75025	[1.618033988957902]
26 -> 121393	[1.6180339886704431]
27 -> 196418	[1.6180339887802426]
28 -> 317811	[1.618033988738303]
29 -> 514229	[1.6180339887543225]
30 -> 832040	[1.6180339887482036]
31 -> 1346269	[1.6180339887505408]
32 -> 2178309	[1.6180339887496482]
33 -> 3524578	[1.618033988749989]
34 -> 5702887	[1.618033988749859]
35 -> 9227465	[1.6180339887499087]
36 -> 14930352	[1.6180339887498896]
37 -> 24157817	[1.618033988749897]
38 -> 39088169	[1.618033988749894]
39 -> 63245986	[1.6180339887498951]
40 -> 102334155	[1.6180339887498947]
41 -> 165580141	[1.618033988749895]
42 -> 267914296	[1.618033988749895]
43 -> 433494437	[1.618033988749895]
44 -> 701408733	[1.618033988749895]
45 -> 1134903170	[1.618033988749895]
46 -> 1836311903	[1.618033988749895]
47 -> 2971215073	[1.618033988749895]
48 -> 4807526976	[1.618033988749895]
49 -> 7778742049	[1.618033988749895]
50 -> 12586269025	[1.618033988749895]
51 -> 20365011074	[1.618033988749895]
52 -> 32951280099	[1.618033988749895]
53 -> 53316291173	[1.618033988749895]
54 -> 86267571272	[1.618033988749895]
55 -> 139583862445	[1.618033988749895]
56 -> 225851433717	[1.618033988749895]
57 -> 365435296162	[1.618033988749895]
58 -> 591286729879	[1.618033988749895]
59 -> 956722026041	[1.618033988749895]
60 -> 1548008755920	[1.618033988749895]
61 -> 2504730781961	[1.618033988749895]
62 -> 4052739537881	[1.618033988749895]
63 -> 6557470319842	[1.618033988749895]
64 -> 10610209857723	[1.618033988749895]
65 -> 17167680177565	[1.618033988749895]
66 -> 27777890035288	[1.618033988749895]
67 -> 44945570212853	[1.618033988749895]
68 -> 72723460248141	[1.618033988749895]
69 -> 117669030460994	[1.618033988749895]
70 -> 190392490709135	[1.618033988749895]
71 -> 308061521170129	[1.618033988749895]
72 -> 498454011879264	[1.618033988749895]
73 -> 806515533049393	[1.618033988749895]
74 -> 1304969544928657	[1.618033988749895]
75 -> 2111485077978050	[1.618033988749895]
76 -> 3416454622906707	[1.618033988749895]
77 -> 5527939700884757	[1.618033988749895]
78 -> 8944394323791464	[1.618033988749895]
79 -> 14472334024676221	[1.618033988749895]
80 -> 23416728348467685	[1.618033988749895]
81 -> 37889062373143906	[1.618033988749895]
82 -> 61305790721611591	[1.618033988749895]
83 -> 99194853094755497	[1.618033988749895]
84 -> 160500643816367088	[1.618033988749895]
85 -> 259695496911122585	[1.618033988749895]
86 -> 420196140727489673	[1.618033988749895]
87 -> 679891637638612258	[1.618033988749895]
88 -> 1100087778366101931	[1.618033988749895]
89 -> 1779979416004714189	[1.618033988749895]
90 -> 2880067194370816120	[1.618033988749895]
91 -> 4660046610375530309	[1.618033988749895]
92 -> 7540113804746346429	[1.618033988749895]
93 -> 12200160415121876738	[1.618033988749895]
94 -> 19740274219868223167	[1.618033988749895]
95 -> 31940434634990099905	[1.618033988749895]
96 -> 51680708854858323072	[1.618033988749895]
97 -> 83621143489848422977	[1.618033988749895]
98 -> 135301852344706746049	[1.618033988749895]
99 -> 218922995834555169026	[1.618033988749895]
100 -> 354224848179261915075	[1.618033988749895]

In [2]: from math import sqrt

In [3]: def testa_phi(n):
   ...:     return ((1 + sqrt(5))/2)**n
   ...: 

In [4]: testa_phi(100) == testa_phi(98) + testa_phi(99)
Out[4]: True

In [5]: def testa_psi(n):
   ...:     return ((1 - sqrt(5))/2)**n

In [6]: testa_psi(100) == testa_psi(98) + testa_psi(99)
Out[6]: False

In [7]: testa_psi(100) - testa_psi(98) + testa_psi(99)
Out[7]: -4.0855789844748035e-21

In [8]: 0.1 + 0.1 + 0.1
Out[8]: 0.30000000000000004

In [9]: phi(10)
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In [9], line 1
----> 1 phi(10)

NameError: name 'phi' is not defined

In [10]: testa_phi(10)
Out[10]: 122.99186938124426

In [11]: testa_psi(100) - (testa_psi(98) + testa_psi(99))
Out[11]: 5.64237288394698e-37

In [12]: testa_phi(100)
Out[12]: 7.920708398483749e+20

In [13]: testa_phi(20)
Out[13]: 15126.999933893048

In [14]: def testa_BLA(n):
    ...:     return 3*testa_phi(n) + 7*testa_psi(n)
    ...: 

In [15]: testa_BLA(100) - (testa_BLA(98) + testa_BLA(99))
Out[15]: 0.0

In [16]: testa_psi(30)
Out[16]: 5.374904998555718e-07

In [17]: testa_psi(20)
Out[17]: 6.610696135189609e-05

In [18]: def Binet(n):
    ...:     return (1/sqrt(5))*(testa_phi(n) + testa_psi(n))
    ...: 

In [19]: Binet(0)
Out[19]: 0.8944271909999159

In [20]: def Binet(n):
    ...:     return (1/sqrt(5))*(testa_phi(n) - testa_psi(n))
    ...: 

In [21]: Binet(0)
Out[21]: 0.0

In [22]: Binet(1)
Out[22]: 1.0

In [23]: for x in range(20):
    ...:     print(f"Binet({x}) = {Binet(x)}")
    ...: 
Binet(0) = 0.0
Binet(1) = 1.0
Binet(2) = 1.0
Binet(3) = 2.0
Binet(4) = 3.0000000000000004
Binet(5) = 5.000000000000001
Binet(6) = 8.000000000000002
Binet(7) = 13.000000000000002
Binet(8) = 21.000000000000004
Binet(9) = 34.00000000000001
Binet(10) = 55.000000000000014
Binet(11) = 89.00000000000003
Binet(12) = 144.00000000000006
Binet(13) = 233.00000000000006
Binet(14) = 377.00000000000017
Binet(15) = 610.0000000000003
Binet(16) = 987.0000000000005
Binet(17) = 1597.000000000001
Binet(18) = 2584.000000000002
Binet(19) = 4181.000000000003

In [24]: a = (13 - 9j)/(0 + 2j)

In [25]: a
Out[25]: (-4.5-6.5j)

In [26]: b = (13 + 9j)/(0 + 2j)

In [27]: b
Out[27]: (4.5-6.5j)

In [28]: a+b
Out[28]: -13j

In [29]: a-b
Out[29]: (-9+0j)

In [30]: a = (13 + 9j)/(0 + 2j)

In [31]: b = (-13 + 9j)/(0 + 2j)

In [32]: a+B
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In [32], line 1
----> 1 a+B

NameError: name 'B' is not defined

In [33]: a+b
Out[33]: (9+0j)

In [34]: a*(0+1j) + b*(0+1j)
Out[34]: 9j

In [35]: a*(0+1j) - b*(0+1j)
Out[35]: (13+0j)

In [36]: def G(n):
    ...:     return a*(0+1j)**n + b*(0+1j)**n
    ...: 

In [37]: for x in range(20):
    ...:     print(f"G({x}) = {G(x)}")
    ...: 
G(0) = (9+0j)
G(1) = 9j
G(2) = (-9+0j)
G(3) = -9j
G(4) = (9+0j)
G(5) = 9j
G(6) = (-9+0j)
G(7) = -9j
G(8) = (9+0j)
G(9) = 9j
G(10) = (-9+0j)
G(11) = -9j
G(12) = (9+0j)
G(13) = 9j
G(14) = (-9+0j)
G(15) = -9j
G(16) = (9+0j)
G(17) = 9j
G(18) = (-9+0j)
G(19) = -9j

In [38]: def G(n):
    ...:     return a*(0+1j)**n + b*(0-1j)**n
    ...: 

In [39]: for x in range(20):
    ...:     print(f"G({x}) = {G(x)}")
    ...: 
G(0) = (9+0j)
G(1) = (13+0j)
G(2) = (-9+0j)
G(3) = (-13+0j)
G(4) = (9+0j)
G(5) = (13+0j)
G(6) = (-9+0j)
G(7) = (-13+0j)
G(8) = (9+0j)
G(9) = (13+0j)
G(10) = (-9+0j)
G(11) = (-13+0j)
G(12) = (9+0j)
G(13) = (13+0j)
G(14) = (-9+0j)
G(15) = (-13+0j)
G(16) = (9+0j)
G(17) = (13+0j)
G(18) = (-9+0j)
G(19) = (-13+0j)

In [40]: