

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
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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/bc/d)==((ac)/(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



