Octahedral number

In number theory, an octahedral number is a figurate number that represents the number of spheres in an octahedron formed from close-packed spheres. The ${\displaystyle n}$th octahedral number ${\displaystyle O_{n}}$ can be obtained by the formula:^[1]

${\displaystyle O_{n}={n(2n^{2}+1) \over 3}.}$

The first few octahedral numbers are:

1, 6, 19, 44, 85, 146, 231, 344, 489, 670, 891 (sequence A005900 in the OEIS).