Centered square number

A centered square number is a number which is the sum of two successive squares. For example, a centered square. The first centered square numbers are

A centered square number quantifies a number of stones, so that a stone is in the center surrounded by other stones so that they form a square.

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

• 2.1 Modifications and Verallgemeinungen

Relations to other figurate numbers

Triangular numbers

The th -centered square number is an odd number that is one greater than four times of the number -th triangle.

Each -th centered square number can be generated as a sum of triangular numbers:

Square numbers

Each centered square number is the sum of two consecutive (distributed ) square numbers. This becomes obvious when one changes the formula for calculating the centered square numbers.

Also at the a centered square number underlying patterns can recognize this situation:

Others

Compared to the squares, which are always assembled there in the sequence of the centered squares some primes. The first prime -centered square numbers are

Modifications and Verallgemeinungen

• The decentralized square and Sechseckszahlen or Polygonalzahlen.
• Oktaederzahlen are the sums of the first -centered square numbers (see Figured number).