A320313 Number of ways to write n as the sum of 4 positive integers a, b, c, d such that d < b and a/b - c/d = (a - c)/(b - d).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 2, 0, 1, 1, 0, 1, 1, 2, 1, 1, 2, 0, 2, 1, 3, 1, 2, 2, 1, 1, 2, 3, 2, 2, 3, 2, 2, 1, 4, 1, 4, 2, 2, 3, 5, 3, 3, 2, 5, 1, 4, 2, 4, 5, 4, 3, 3, 4, 4, 3, 3, 3, 6, 2, 5, 4, 7, 3, 9, 3, 4, 3, 5

Offset: 1

Author

Hugo Pfoertner, Oct 10 2018

Keywords

• nonn

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A026810, A319853, A319854, A320311, A320312.

Programs

PARI

m=86;v=vector(m);for(a=1,m,for(b=1,m,for(c=1,m,for(d=1,b-1,n=a+b+c+d;if(n<=m,if(a/b-c/d==(a-c)/(b-d),v[n]++))))));v