Decagonal number
A decagonal number is a figurate number that extends the concept of triangular and square numbers to the decagon. However, unlike the triangular and square numbers, the patterns involved in the construction of decagonal numbers are not rotationally symmetrical. Specifically, the nth decagonal numbers counts the number of dots in a pattern of n nested decagons, all sharing a common corner, where the ith decagon in the pattern has sides made of i dots spaced one unit apart from each other. The n-th decagonal number is given by the formula
The first few decagonal numbers are:
The nth decagonal number can also be calculated by adding the square of n to thrice the th pronic number or, to put it algebraically, asProperties
