Centered tetrahedral number explained

Number:

Parentsequence:

Polyhedral numbers

Formula:

	(2n+1)(n²⁺ⁿ⁺³⁾
	3

First Terms:

1, 5, 15, 35, 69, 121, 195

Oeis:

A005894

Oeis Name:

Centered tetrahedral

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

th centered tetrahedral number, starting at

n=0

for a single dot, is:^[1]

The first such numbers are:

Notes and References

Deza numbers the centered tetrahedral numbers at
n=1

for a single dot, leading to a different formula.