A394296 - OEIS

A394296

a(n) is the number of unit cubes in the cubic lattice, divided by 24, that have 3 vertices strictly inside and 5 vertices strictly outside the sphere (x-1/2)^2 + (y-1/2)^2 + (z-1/2)^2 = n, i.e., the sphere centered at the deep hole.

%I #8 Mar 17 2026 15:19:41

%S 0,0,0,0,0,1,1,0,0,1,1,0,0,2,2,2,2,0,0,2,2,1,1,2,2,2,2,4,4,1,1,2,2,3,

%T 3,2,2,4,4,2,2,4,4,4,4,3,3,4,4,3,3,4,4,5,5,4,4,4,4,5,5,3,3,8,8,5,5,5,

%U 5,4,4,4,4,8,8,5,5,6,6,8,8,6,6,3,3,8,8,10,10,5,5

%N a(n) is the number of unit cubes in the cubic lattice, divided by 24, that have 3 vertices strictly inside and 5 vertices strictly outside the sphere (x-1/2)^2 + (y-1/2)^2 + (z-1/2)^2 = n, i.e., the sphere centered at the deep hole.

%H Hugo Pfoertner, <a href="/A394296/b394296.txt">Table of n, a(n) for n = 0..10000</a>

%Y Cf. A005878, A393823, A394294, A394295, A394297, A394304, A394305, A394306.

%K nonn

%O 0,14

%A _Hugo Pfoertner_, Mar 15 2026