An octahedral number counts the points stacked in a regular octahedron (two square pyramids glued base to base), given by \(k(2k^2+1)/3\). The sequence: 1, 6, 19, 44, 85, 146, 231, 344, 489, 670.
It's one of the Platonic-solid figurate families. A neat identity: each octahedral number is the sum of two consecutive [[square-pyramidal]] numbers, and the octahedral numbers are also the difference of two consecutive cubes' worth of centered pattern. Pollock's conjecture (1850) — still unproven — says every positive integer is a sum of at most seven octahedral numbers.