326 magic square

Taken from an 18th-century blockbook version of the Book of Changes, or the I Ching, the left diagram depicts the Lho shu magic square.

(Photo courtesy of C. Walker/Topham/The Image Works)

It is straightforward to compute the magic constant

Mof a standard n×nmagic square. Adding the entries

in each row produces the magic constant Mand, as

there are nrows, the quantity nM must equal the sum

of all the entries in the table. Thus, as the

SUMS OF

POWERS

formulae show:

yielding:

For n= 1, 2, 3, 4, 5, … this gives the sequence of val-

ues 1,5,15,34,65,…