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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).

%I A320313 #8 Oct 11 2018 12:03:22
%S A320313 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,
%T A320313 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,
%U A320313 3,3,4,4,3,3,3,6,2,5,4,7,3,9,3,4,3,5
%N 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).
%H A320313 Hugo Pfoertner, <a href="/A320313/b320313.txt">Table of n, a(n) for n = 1..1000</a>
%o A320313 (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
%Y A320313 Cf. A026810, A319853, A319854, A320311, A320312.
%K A320313 nonn
%O A320313 1,22
%A A320313 _Hugo Pfoertner_, Oct 10 2018