56 



MAJOK P. A. MACMAHON: MEMOIK ON THE 



ORDER 6. 

 1= 1 2 3 4 5 6 







Art. 143. I now proceed to consider the enumeration of the squares of even 

 order 2n, such that every row and column contains two units, and the dexter and 

 sinister diagonals / and m units respectively. 



I form the product 



n 



CC-2 



< 2 > 



where 2 <s) is the sum two together of the quantities 



and I seek the coefficient, a function of X and /x, of 



(ajOa^.o^) 8 



in the product. 



The coefficient of X'/u, in the sought function of X and p. is the required number. 

 Let pi, p 2 he the sum and the sum two together of the quantities 



then 



whence 



+ 2 (Xyx-1) 



+ terms involving powers of 1; 2;1 above the second. 



