Centered Square Number

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 , 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

REFERENCES:

Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, p. 41, 1996.

Sloane, N. J. A. Sequence A001844/M3826 in "The On-Line Encyclopedia of Integer Sequences."