The number of cells in a generalized Chinese checkers board (or ``centered'' Hexagram).

(1) |

The first Triangular star numbers are 1, 253, 49141, 9533161, ... (Sloane's A006060), and can
be computed using

(2) | |||

(3) |

The first few Square star numbers are 1, 121, 11881, 1164241, 114083761, ... (Sloane's A006061).
Square star numbers are obtained by solving the Diophantine Equation

(4) |

(5) |

**References**

Gardner, M. ``Hexes and Stars.'' Ch. 2 in *Time Travel and Other Mathematical Bewilderments.* New York: W. H. Freeman, 1988.

Hindin, H. ``Stars, Hexes, Triangular Numbers, and Pythagorean Triples.'' *J. Recr. Math.* **16**, 191-193, 1983-1984.

Sloane, N. J. A. Sequences
A003154/M4893,
A006060/M5425, and
A006061/M5385
in ``An On-Line Version of the Encyclopedia of Integer Sequences.''
http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.
*The Encyclopedia of Integer Sequences.* San Diego: Academic Press, 1995.

© 1996-9

1999-05-26