A048259 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.

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, 22, 7, 33, 8, 24, 16, 16, 16, 39, 9, 18, 19, 38, 9, 41, 10, 28, 28, 20, 10, 57, 15, 30, 21, 32, 11, 43, 20, 46, 24, 24, 12, 77, 13, 26, 35, 42, 23, 53, 14, 38, 26, 52, 14, 83

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Examples

			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).
		

Links

• Sean A. Irvine, Java program (github)

Crossrefs

Cf. A007997, A007998, A003050, A003051.

Programs

PARI

iscanon(n,v)={for(d=1, n-1, if(gcd(n,d)==1 && lex(v,vecsort(v*d%n))>0, return(0))); 1}
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

Extensions

a(42) onward corrected by Sean A. Irvine, Jun 10 2021