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
Famous quotes containing the words formula and/or sequence:
“My formula for greatness in human beings is amor fati: that one wants to change nothing, neither forwards, nor backwards, nor in all eternity. Not merely to endure necessity, still less to hide it—all idealism is mendacity in the face of necessity—but rather to love it.”
—Friedrich Nietzsche (1844–1900)
“We have defined a story as a narrative of events arranged in their time-sequence. A plot is also a narrative of events, the emphasis falling on causality. “The king died and then the queen died” is a story. “The king died, and then the queen died of grief” is a plot. The time sequence is preserved, but the sense of causality overshadows it.”
—E.M. (Edward Morgan)