Centered cube number

A centered cubic number is a number that is the sum of two successive cubes. For example, a centered cubic number. The first centered cubes are

The centered cube numbers are the spatial extension of the centered square numbers in the third dimension.

Calculation

The te - centered cubic number is calculated according to the formula

Relations to other figurate numbers

The te - centered cubic number is the sum of the first -centered square numbers.

Properties

• All centered cubic numbers are odd.
• It is true, where the- th square Pyramidalzahl is:

• The sum of the reciprocals of the centered cubic numbers, so is convergent.
• The shape of centered cubes occurs in nature in the structure of atoms.

Generating function

The function

Contains in its expansion on the left side of the equation, the result of centered cubes. It is therefore referred to as a generating function of the sequence of centered cubes.