Centered pentagonal number

The centered pentagonal belong to the centered Polygonalzahlen, ie there are two-dimensional Figured numbers. They quantify the number of blocks with which it is possible to design a pentagon according to the following scheme:

There is a stone in the center and around that gradually more stones are then placed, namely successively 5, 10, 15, etc., so that a pentagon.

The first centered pentagonal are

For some authors, the 0 also figured as a zeroth number is one of them.

Calculation

The te - figured number is

If you 1 defined as the first centered Fünfeckszahl.

Alternatively, they can be calculated with the triangular numbers by

More

Generating function

The result of the centered pentagonal have a generating function, namely

Related figuierte numbers

• The ( decentralized ) pentagonal refer to another way of laying stones to pentagons:

The fourth decentralized Fünfeckszahl 22

The fourth centered Fünfeckszahl 31

• If, in accordance to this pattern no pentagons but three-, four -, or hexagons we obtain the other centered Polygonalzahlen or Polygonalzahlen.

See also Figured number