Centered icosahedral number

Totalno. of terms	Infinity
Subsequence of	Polyhedral numbers
Formula	${\displaystyle \frac{(2n+1)(5n^2+5n+3)}{3}}$
First terms	1,13,55,147,309,561,923
OEIS index	A005902 Centered icosahedral

Inmathematics, thecentered icosahedral numbers also known ascuboctahedral numbers are a sequence of numbers, describing two different representations for these numbers as three-dimensionalfigurate numbers. As centered icosahedral numbers, they arecentered numbers representing points arranged in the shape of aregular icosahedron. As cuboctahedral numbers, they represent points arranged in the shape of acuboctahedron, and are amagic number for theface-centered cubic lattice. The centered icosahedral number for a specific${\displaystyle n}$ is given by$${\displaystyle \frac{(2n+1)\left(5n^2+5n+3\right)}{3}.}$$

The first such numbers are

• Sloane, N. J. A. (ed.)."Sequence A005902 (Centered icosahedral (or cuboctahedral) numbers, also crystal ball sequence for f.c.c. lattice)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation..

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