A320311 Number of ways to write n as the sum of 4 positive integers a, b, c, d such that 1 - a/c = (1 - b/d)^2.

0, 0, 0, 1, 0, 2, 0, 3, 0, 5, 0, 6, 1, 6, 0, 8, 2, 9, 2, 10, 0, 15, 1, 14, 1, 15, 3, 15, 2, 17, 4, 19, 3, 21, 1, 21, 4, 26, 3, 25, 4, 24, 4, 27, 6, 29, 5, 31, 5, 30, 4, 36, 4, 37, 6, 34, 6, 41, 8, 36, 8, 43, 4, 42, 5, 44, 10, 44, 9, 45, 9, 45, 10, 48

Offset: 1

Author

Hugo Pfoertner and Rainer Rosenthal Oct 10 2018

Keywords

• nonn

Crossrefs

Cf. A026810, A319853, A319854, 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(1-a/c==(1-b/d)^2,v[n]++))))));v