A319853 Number of ways to write n as the sum of 4 positive integers a,b,c,d such that a/b - c/d = (a - c)/(b + d).

0, 0, 0, 1, 0, 2, 0, 5, 0, 4, 2, 5, 2, 10, 0, 9, 2, 14, 2, 11, 2, 16, 6, 15, 2, 18, 4, 21, 4, 18, 6, 27, 6, 24, 4, 27, 6, 32, 8, 25, 8, 32, 10, 39, 4, 36, 8, 35, 10, 42, 10, 37, 12, 42, 6, 45, 14, 52, 14, 41, 12, 52, 10, 55, 12, 54, 14, 57, 12, 52, 20, 59, 14, 68

Offset: 1

Author

Hugo Pfoertner and Rainer Rosenthal, Sep 29 2018

Keywords

• nonn

Examples

			a(4) = 1: 1/1 - 1/1 = (1 - 1)/(1 + 1);
a(6) = 2: 1/2 - 1/2 = (1 - 1)/(2 + 2), 2/1 - 2/1 = (2 - 2)/(1 + 1);
a(8) = 5: 1/1 - 4/2 = (1 - 4)/(1 + 2), 1/3 - 1/3 = (1 - 1)/(3 + 3),
          2/2 - 2/2 = (2 - 2)/(2 + 2), 3/1 - 3/1 = (3 - 3)/(1 + 1),
          4/2 - 1/1 = (4 - 1)/(2 + 1).
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A026810, A319854, A320311, A320312, A320313.

Programs

PARI

m=74;v=vector(m);for(a=1,m,for(b=1,m,for(c=1,m,for(d=1,m,n=a+b+c+d;if(n<=m,if((a/b-c/d)==((a-c)/(b+d)),v[n]++))))));v