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

0,3

Links

Table of n, a(n) for n=0..72.

Sean A. Irvine, Java program (github)

Example

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).

Prog

(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

Crossrefs

Cf. A007997, A007998, A003050, A003051.

Sequence in context: A217536 A333618 A058267 * A324150 A198461 A228576

Adjacent sequences: A048256 A048257 A048258 * A048260 A048261 A048262

Keyword

nonn

Author

N. J. A. Sloane

Extensions

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

Status

approved