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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).

%I A319853 #16 Oct 15 2018 07:50:17
%S A319853 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,
%T A319853 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,
%U A319853 14,52,14,41,12,52,10,55,12,54,14,57,12,52,20,59,14,68
%N 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).
%H A319853 Hugo Pfoertner, <a href="/A319853/b319853.txt">Table of n, a(n) for n = 1..500</a>
%e A319853 a(4) = 1: 1/1 - 1/1 = (1 - 1)/(1 + 1);
%e A319853 a(6) = 2: 1/2 - 1/2 = (1 - 1)/(2 + 2), 2/1 - 2/1 = (2 - 2)/(1 + 1);
%e A319853 a(8) = 5: 1/1 - 4/2 = (1 - 4)/(1 + 2), 1/3 - 1/3 = (1 - 1)/(3 + 3),
%e A319853           2/2 - 2/2 = (2 - 2)/(2 + 2), 3/1 - 3/1 = (3 - 3)/(1 + 1),
%e A319853           4/2 - 1/1 = (4 - 1)/(2 + 1).
%o A319853 (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
%Y A319853 Cf. A026810, A319854, A320311, A320312, A320313.
%K A319853 nonn
%O A319853 1,6
%A A319853 _Hugo Pfoertner_ and _Rainer Rosenthal_, Sep 29 2018