n+1
The number of states of an n + 1- exagon is equal to the nth member of this sequence. The super variant of this sequence counts lattice paths with diagonal steps, as opposed to this sequence, which counts p-good paths. This sequence obeys the recurrence relation that the nth element of this sequence is equal to the sum over the rst n−1 elements of SkSn−k−1, and the nth element of this sequence gives the number of binary bracketings of n + 1 letters. The nth element of this sequence gives the number of ways that a regular n-gon can be divided into n − 2 triangles if orientation matters. For ten points, identify this sequence named for a Belgian mathematician whose nth element is equal to 1 times 2n choose n. n+1
The number of states of an n + 1- exagon is equal to the nth member of this sequence.
Catalan sequence 