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A320312 Number of ways to write n as the sum of 4 positive integers a, b, c, d such that b != d and a/b - c/d = (a - c)/(b - d).

%I A320312 #8 Oct 12 2018 12:14:58
%S A320312 0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,2,1,2,1,0,5,1,3,1,3,3,2,2,3,4,4,3,5,
%T A320312 1,4,4,8,3,6,4,4,4,6,6,7,5,8,5,6,4,11,4,11,6,7,6,13,8,7,8,13,4,11,5,
%U A320312 12,10,11,9,11,9,10,10,12,7,18,6,15,10,15
%N A320312 Number of ways to write n as the sum of 4 positive integers a, b, c, d such that b != d and a/b - c/d = (a - c)/(b - d).
%H A320312 Hugo Pfoertner, <a href="/A320312/b320312.txt">Table of n, a(n) for n = 1..1000</a>
%o A320312 (PARI) m=80;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(b!=d&&a/b-c/d==(a-c)/(b-d),v[n]++))))));v
%Y A320312 Cf. A026810, A319853, A319854, A320311, A320313.
%K A320312 nonn
%O A320312 1,17
%A A320312 _Hugo Pfoertner_, Oct 10 2018