The lazy caterer's sequence gives the maximum number of pieces you can divide a disc (a pancake, a pizza) into using \(k\) straight cuts: 1, 2, 4, 7, 11, 16, 22, 29, 37, 46. Each new cut adds as many pieces as it crosses existing cuts, so the \(k\)-th cut adds \(k\) pieces — making each term one more than a [[triangular]] number.
The three-dimensional version (slicing a cake with planar cuts) gives the [[cake]] numbers. The name comes from a caterer too lazy to rearrange the slices between cuts.