Rabbits etc. Fibonacci.

A certain man put a pair of rabbits in a place surrounded on all sides by a wall. How many pairs of rabbits can be produced from that pair in a year if it is supposed that every month each pair begets a new pair which from the second month on becomes productive?

leonardo-fibonacci rabbig

The resulting numbers of rabbits, month by month form a series known as the Fibonacci series.

I wrote a little program to work out… ooh… 1000 months worth of rabbits. Fibonacci to 1000 iterations

This is the first 100

1
1
2
3
5
8
13
21
34
55
89
144
233
377
610
987
1597
2584
4181
6765
10946
17711
28657
46368
75025
121393
196418
317811
514229
832040
1346269
2178309
3524578
5702887
9227465
14930352
24157817
39088169
63245986
102334155
165580141
267914296
433494437
701408733
1134903170
1836311903
2971215073
4807526976
7778742049
12586269025
20365011074
32951280099
53316291173
86267571272
139583862445
225851433717
365435296162
591286729879
956722026041
1548008755920
2504730781961
4052739537881
6557470319842
10610209857723
17167680177565
27777890035288
44945570212853
72723460248141
117669030460994
190392490709135
308061521170129
498454011879264
806515533049393
1304969544928657
2111485077978050
3416454622906707
5527939700884757
8944394323791464
14472334024676220
23416728348467684
37889062373143904
61305790721611592
99194853094755504
160500643816367104
259695496911122592
420196140727489664
679891637638612224
1100087778366101888
1779979416004714240
2880067194370816000
4660046610375530496
7540113804746346496
12200160415121876992
19740274219868225536
31940434634990100480
51680708854858326016
83621143489848426496
135301852344706760704
218922995834555203584
354224848179261997056
573147844013817200640
927372692193079197696

After that, it gets big. If you left the imaginary rabbits for 1000 months (83 years), you’d wind up with this many:

113796925398360201953926115553645816970640849573127786938719328994329376466419959011035655716823855099924191763168213527616175814941274433735102538426038875847839692485942437387020099603495346028508770329427968

 

Which in my day was considered to be a great deal of rabbits.

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