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Centered Square Number

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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, ... (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


See also Centered Pentagonal Number, Centered Polygonal Number, Centered Triangular Number, Square Number


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 ``An On-Line Version of the Encyclopedia of Integer Sequences.'' and Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.

© 1996-9 Eric W. Weisstein