A New Proof of the Formula for the Number of 3 × 3 Magic Squares
Miklós Bóna · Mathematics Magazine · 1997
Introduction For our purposes, a magic square is a square matrix with nonnegative integer entries in which all row sums and column sums are equal. (We note that other notions of magic squares exist. For example, one might require that the diagonal sums be the same, too, or one might forbid repetitions of elements in any line.) L,et H,(r) denote the number of n X n magic squares of line sum r. It has long been known (see [1] and [4]) that