The On-Line Encyclopedia of Integer Sequences (OEIS)

A048259 revision #15

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

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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