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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). 5

%I #8 Oct 12 2018 12:14:58

%S 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 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 12,10,11,9,11,9,10,10,12,7,18,6,15,10,15

%N 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 Hugo Pfoertner, <a href="/A320312/b320312.txt">Table of n, a(n) for n = 1..1000</a>

%o (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 Cf. A026810, A319853, A319854, A320311, A320313.

%K nonn

%O 1,17

%A _Hugo Pfoertner_, Oct 10 2018

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