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 
th term is 
, and the first few such numbers for 
, 1, 2, ... are 1, 4, 10, 19, 31, 46, 64, ... (Sloane's A005448). The generating function giving the centered triangular numbers is
th term is , and the first few such numbers for , 1, 2, ... are 1, 4, 10, 19, 31, 46, 64, ... (Sloane's A005448). The generating function giving the centered triangular numbers is Ref: mathworld.wolfram.com |
, and the first few such numbers are 1, 5, 13, 25, 41, ... (Sloane's A001844). Centered square numbers are the sum of two consecutive square numbers and are congruent to 1 (mod 4). The generating function giving the centered square numbers is
, and the first few such numbers are 1, 6, 16, 31, 51, 76, ... (Sloane's A005891). The generating function of the centered pentagonal numbers is
