Statements (13)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
Figurate number
|
| gptkbp:application |
Used in recreational mathematics and number theory
|
| gptkbp:defines |
A centered polygonal number is a centered figurate number that represents a polygon with a dot in the center and all other dots surrounding the center in successive polygonal layers.
|
| gptkbp:example |
Centered triangular numbers, centered square numbers, centered pentagonal numbers, centered hexagonal numbers
|
| gptkbp:first_terms |
1
|
| gptkbp:form |
C_{k,n} = 1 + k*n*(n-1)/2, where k is the number of polygon sides and n is the layer number
|
| https://www.w3.org/2000/01/rdf-schema#label |
Centered polygonal numbers
|
| gptkbp:OEIS |
A001844 (centered square numbers), A005448 (centered hexagonal numbers), etc.
|
| gptkbp:property |
Each centered polygonal number is one more than a multiple of the corresponding ordinary polygonal number.
|
| gptkbp:sequence |
Integer sequence
|
| gptkbp:subclassOf |
gptkb:Centered_figurate_number
|
| gptkbp:bfsParent |
gptkb:Polygonal_numbers
|
| gptkbp:bfsLayer |
7
|