pentagonal numbers
nounUK /pɛnˈtæɡənəl ˈnʌmbəz/
US /pɛnˈtæɡənəl ˈnʌmbərz/
Pentagonal numbers are numbers you can make into a five-sided shape with dots.
The first few pentagonal numbers are 1, 5, 12, 22, and 35.
OTHER MEANINGS
2. A sequence in which each term is the sum of a square number and a triangular number.
Each pentagonal number equals a square number plus a triangular number.
3. Numbers of the form n(3n−1)/2 for whole numbers n.
Using the formula n(3n−1)/2 with n=4 gives the pentagonal number 22.
4. A type of figurate number that generalizes the idea of counting dots in nested pentagons.
Pentagonal numbers belong to the family of figurate numbers.