The number of different triangles which have integer side lengths and perimeter n is T(n) | = | P(n, 3) - sum_(1<=j<=⌊n/2⌋) P(j, 2) | = | [n^2/12] - ⌊n/4 ⌋⌊(n + 2)/4 ⌋ | = | {[n^2/48] | for n even [(n + 3)^2/48] | for n odd, auto right match

Alcuin's sequence | Heronian tetrahedron | Heronian triangle | perfect cuboid | triangle | triangle dissection