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Calculators for Fibonacci (scroll down) and other Sequences

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To start with a dubious assumption: any given pair of baby rabbits don't breed in their first two months. In their third month, however (and every month after that) they produce another pair.

Unsurprisingly, this situation produces a very familiar recurrence relationship: The number of baby rabbits in month n clearly equals the total number of rabbits in month n - 2.

Hence U(n) = U(n-2) + U(n-1)

...Suppose that I very misguidedly decide that my rabbitbreeding is going too slowly: in the second month I buy two more pairs of babyrabbits. How many pairs do I have as time goes on?

Month:

Number of pairs :

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Imagine that the rabbits' fertility was delayed by an extra month. What impact would that have?

Month:

Number of Pairs:

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(For Good Measure, a Padovan Sequence Calculator!)

N:

Result:

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Now for the Fibonacci series itself!

I start with a pair of rabbits, and leave them to their own devices.

How many pairs do I have in the third month? Or the fourth month? The 54th month? Even, in a very hypothetical sort of way, the minus-54th month? Have a go on the calculator below, and see the happy couples appear (doesn't work in Mozilla Firefox - sorry!) before your eyes...

 Months Allowed:    Number of pairs: plenilune@hotmail.co.uk © T. Hutty 2006