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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). 5
 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, 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, 14, 52, 14, 41, 12, 52, 10, 55, 12, 54, 14, 57, 12, 52, 20, 59, 14, 68 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 LINKS Hugo Pfoertner, Table of n, a(n) for n = 1..500 EXAMPLE a(4) = 1: 1/1 - 1/1 = (1 - 1)/(1 + 1); a(6) = 2: 1/2 - 1/2 = (1 - 1)/(2 + 2), 2/1 - 2/1 = (2 - 2)/(1 + 1); a(8) = 5: 1/1 - 4/2 = (1 - 4)/(1 + 2), 1/3 - 1/3 = (1 - 1)/(3 + 3),           2/2 - 2/2 = (2 - 2)/(2 + 2), 3/1 - 3/1 = (3 - 3)/(1 + 1),           4/2 - 1/1 = (4 - 1)/(2 + 1). PROG (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 CROSSREFS Cf. A026810, A319854, A320311, A320312, A320313. Sequence in context: A019962 A086131 A318889 * A228620 A257013 A104755 Adjacent sequences:  A319850 A319851 A319852 * A319854 A319855 A319856 KEYWORD nonn AUTHOR Hugo Pfoertner and Rainer Rosenthal, Sep 29 2018 STATUS approved

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Last modified July 29 22:13 EDT 2021. Contains 346346 sequences. (Running on oeis4.)