Centered tetrahedral number

In mathematics, a centered tetrahedral number is a centered figurate number that represents a tetrahedron. That is, it counts the dots in a three-dimensional dot pattern with a single dot surrounded by tetrahedral shells. The ${\displaystyle n}$th centered tetrahedral number, starting at ${\displaystyle n=0}$for a single dot, is:

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

The first such numbers are: