Centered icosahedral number explained

Number:	Infinity
Parentsequence:	Polyhedral numbers
Formula:	(( 2 n +1 )( 5 n ^{2+5n+3)})/(3)
First Terms:	1, 13, 55, 147, 309, 561, 923
Oeis:	A005902
Oeis Name:	Centered icosahedral

The centered icosahedral numbers and cuboctahedral numbers are two different names for the same sequence of numbers, describing two different representations for these numbers as three-dimensional figurate numbers. As centered icosahedral numbers, they are centered numbers representing points arranged in the shape of a regular icosahedron. As cuboctahedral numbers, they represent points arranged in the shape of a cuboctahedron, and are a magic number for the face-centered cubic lattice. The centered icosahedral number for a specific

n is given by $$\backslash frac.$$

The first such numbers are

References

• Centered icosahedral (or cuboctahedral) numbers, also crystal ball sequence for f.c.c. lattice. .