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 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


See also

Aztec Diamond, Centered Pentagonal Number, Centered Polygonal Number, Centered Triangular Number, Diamond, Hex Number, Square Number

Explore with Wolfram|Alpha


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."

Referenced on Wolfram|Alpha

Centered Square Number

Cite this as:

Weisstein, Eric W. "Centered Square Number." From MathWorld--A Wolfram Web Resource.

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