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That is part of the famous Fibonacci series, in which each number is the sum of the two number preceding it. This series shows up in various places in math and in the world of living things. The next two numbers are 21 and 34.

However, it would be equally true to say that the next two numbers are 11 and 12.

If you use the rule Un = (-n4 + 14n3 - 59n2 + 118n - 48)/24 for n = 1, 2, 3, ...

then U7 = 11 and U8 = 12

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