A centered polygonal number consisting of a central dot with four dots around it, and then additional dots in the gaps between adjacent dots. The general term is n^2 + (n + 1)^2, and the first few such numbers are 1, 5, 13, 25, 41, ... (OEIS 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 (x + 1)^2/(1 - x)^3 = 1 + 5x + 13x^2 + 25x^3 + ....

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