This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
The permutation sums for n=2 are (1,2) + (1,2) = (2,4); (1,2) + (2,1) = (2,1) + (1,2) = (3,3); (2,1) + (2,1) = (4,2); so a(2)=3.
def a381244(n): return HyperplaneArrangements(QQ,tuple(f'x{i}' for i in range(n)))([[list(r),0] for p in Permutations(n) for r in Permutations([p[i]-i-1 for i in range(n)]) if vector(r)>0]).n_regions()
For n = 3, there are A019589(3) = 5 difference vectors up to permutation of components: (-2, 0, 2), (-2, 1, 1), (-1, -1, 2), (-1, 0, 1), and (0, 0, 0). However, (-2, 0, 2) and (-1, 0, 1) are the same up to a factor 2, and (-2, 1, 1) and (-1, -1, 2) are the same up to negation and reversing the order. Hence, a(3) = 3.
For n = 3, there are A019589(3) = 5 difference vectors up to permutation of components: (-2, 0, 2), (-2, 1, 1), (-1, -1, 2), (-1, 0, 1), and (0, 0, 0). However, (-2, 0, 2) and (-1, 0, 1) are the same up to a factor 2. Hence, a(3) = 4.
Comments