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%I #15 Jun 11 2021 18:31:53
%S 1,1,2,3,4,3,7,4,8,6,8,4,15,5,10,11,14,5,17,6,18,14,12,6,31,9,14,13,
%T 22,7,33,8,24,16,16,16,39,9,18,19,38,9,41,10,28,28,20,10,57,15,30,21,
%U 32,11,43,20,46,24,24,12,77,13,26,35,42,23,53,14,38,26,52,14,83
%N Number of distinct solutions to x + y + z = 0 (mod n), where two solutions are equivalent if one can be obtained from the other by multiplying by units in Z/nZ and permuting x,y,z.
%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a048/A048259.java">Java program</a> (github)
%e For n=6 the 7 solutions are (x,y,z) = (0,0,0), (5,1,0), (4,2,0), (4,1,1), (3,3,0), (3,2,1), (2,2,2).
%o (PARI)
%o iscanon(n,v)={for(d=1, n-1, if(gcd(n,d)==1 && lex(v,vecsort(v*d%n))>0, return(0))); 1}
%o a(n)={if(n==0, 1, sum(x=0, n-1, sum(y=x, n-1, my(z=(-x-y)%n); y<=z && iscanon(n,[x,y,z]) )))} \\ _Andrew Howroyd_, Jun 11 2021
%Y Cf. A007997, A007998, A003050, A003051.
%K nonn
%O 0,3
%A _N. J. A. Sloane_
%E a(42) onward corrected by _Sean A. Irvine_, Jun 10 2021
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