Formula and Sequence
The maximum number p of pieces that can be created with a given number of cuts n, where n ≥ 0, is given by the formula
Using binomial coefficients, the formula can be expressed as
This sequence (sequence A000124 in OEIS), starting with, results in
- 1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191, 211, ...
Each number equals 1 plus a triangular number.
Read more about this topic: Lazy Caterer's Sequence
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—Friedrich Nietzsche (1844–1900)
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