lazy caterer’s sequence
Given a pancake (or a circle), how can one cut pieces (not necessarily of the same size) with the minimum number of cuts? For example, to cut a pancake into four pieces, four cuts could be made, each starting at the center and going to the edge. But it would be much simpler to make just two cuts to cut it into four pieces.
The maximum number of pieces that can be created with a given number of cuts is given by the formula
which gives the lazy caterer’s sequence: 1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, … (listed in A000124 of Sloane’s OEIS).
Shel Kaphan, in a remark to the OEIS writes that ”when constructing a zonohedron, one zone at a time, out of (up to) 3-D non-intersecting parallelepipeds, the th element of this sequence is the number of edges in the th zone added with the th layer of parallelepipeds.”
|Title||lazy caterer’s sequence|
|Date of creation||2013-03-22 16:16:54|
|Last modified on||2013-03-22 16:16:54|
|Last modified by||PrimeFan (13766)|
|Synonym||lazy caterers sequence|
|Synonym||circle cutting problem|
|Synonym||pancake cutting problem|
|Defines||central polygonal number|