Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
Figurate number
Integer sequence |
| gptkbp:definedIn |
P(n) = n(3n-1)/2
|
| gptkbp:differenceBetweenTerms |
3n-2
|
| gptkbp:first_terms |
1
12 22 35 5 |
| gptkbp:generalizes |
gptkb:Polygonal_numbers
|
| https://www.w3.org/2000/01/rdf-schema#label |
Pentagonal numbers
|
| gptkbp:inverseFormula |
n = (sqrt(24x+1)+1)/6
|
| gptkbp:namedAfter |
gptkb:Pentagon
|
| gptkbp:OEIS |
A000326
|
| gptkbp:property |
Every pentagonal number is a centered nonagonal number
All pentagonal numbers are congruent to 0, 1, or 2 mod 5 |
| gptkbp:recurrence |
P(n) = P(n-1) + 3n - 2
|
| gptkbp:relatedTo |
gptkb:Hexagonal_numbers
gptkb:Triangular_numbers |
| gptkbp:usedIn |
Partition function
|
| gptkbp:visualizes |
Dots arranged in pentagon shape
|
| gptkbp:bfsParent |
gptkb:Polygonal_numbers
|
| gptkbp:bfsLayer |
7
|