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The next number is 1.

The simplest polynomial rule is

Un = (-15n4 + 202n3 - 921n2 + 1646n - 888)/24 for n = 1, 2, 3, ...

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What is the rule for the Fibonacci sequence?

The rule of the Fibonacci sequence is simple. Take the previous number in the sequence, and add it to the current number. The sequence starts with 0 and 1. 0, 1 So, add 0+1=1. The sequence now contains three numbers. 0, 1, 1 Now, add 1+1=2. This brings us to four numbers. 0, 1, 1, 2 Add 1 and 2. (1+2=3) 0, 1, 1, 2, 3 Now it gets a bit tricky. Add 2+3=5, so the next number is 5. 0, 1, 1, 2, 3, 5 Continue to add the numbers accordingly. (3+5=8) 0, 1, 1, 2, 3, 5, 8 Proceed. 0, 1, 1, 2, 3, 5, 8, 13, 25, 38, 63, 101, 164...


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A recursive sequence uses previous numbers to find the next number in a sequence after the base case. The Fibonacci sequence is an example of such a sequence. The base numbers of the Fibonacci sequence are 0 and 1. After that base, you find the next number in the sequence by adding the two previous numbers. So, the Fibonacci sequence looks like so: 0, 1, 1, 2, 3, 5, 8.... So, the third number is found by adding the first and second numbers, 0 and 1. So the third number is 1. The fourth number is found by adding the second and third numbers, 1 and 1. So, the fourth number is 2. You can continue on this way forever.