Trimagic squares (Christian Boyer)

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given n, put the first n*n integers into a n*n square-grid such that the number of trimagic lines is maximal. Lines are : n rows, n columns , 2 diagonals. A line a(1)..a(n) is trimagic, iff n/2*(1+n*n) = Sum a(i) and n/6*(1+n*n)(2*n*n+1) = Sum a(i)^2 and n^3/4*(1+n*n)^2 = Sum a(i)^3 http://cboyer.club.fr/multimagie/English/Problems.htm For every N=1...50, compute a square where the maximum number of rows, columns and diagonals are trimagic.