Lazy Caterer's Sequence - Formula and Sequence

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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