A centered triangular number is a centered polygonal number consisting of a central dot with three dots around it, and then additional dots in the gaps between adjacent dots. The nth term is (3n^2 + 3n + 2)/2, and the first few such numbers for n = 0, 1, 2, ... are 1, 4, 10, 19, 31, 46, 64, ... (OEIS A005448). The generating function giving the centered triangular numbers is (x^2 + x + 1)/(1 - x)^3 = 1 + 4x + 10x^2 + 19x^3 + ....

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