A centered polygonal number consisting of a central dot with five dots around it, and then additional dots in the gaps between adjacent dots. The general term is (5n^2 + 5n + 2)/2, and the first few such numbers are 1, 6, 16, 31, 51, 76, ... (OEIS A005891). The generating function of the centered pentagonal numbers is (x^2 + 3x + 1)/(1 - x)^3 = 1 + 6x + 16x^2 + 31x^3 + ....

centered polygonal number | centered square number | centered triangular number | hex number | pentagonal number