A078593 Number of pairs (x,y) 1<=x<=y<=n such that 1/x+1/y+1/n < 1/2.

0, 0, 0, 0, 0, 0, 4, 9, 16, 24, 33, 42, 55, 68, 81, 96, 111, 127, 145, 163, 183, 203, 224, 246, 270, 294, 319, 345, 372, 400, 429, 459, 490, 522, 555, 589, 624, 660, 697, 735, 774, 814, 856, 898, 941, 985, 1030, 1076, 1123, 1171, 1220, 1270, 1321, 1373, 1426

Offset

1,7

Links

Table of n, a(n) for n=1..55.

Formula

for n>=43 a(n) = (1/2)*(n^2 - 3*n - 8 )

Prog

(PARI) a(n)=sum(i=1, n, sum(j=1, i, if(sign(1/i+1/j+1/n-1/2)+1, 0, 1)))

Crossrefs

Sequence in context: A378489 A320891 A161697 * A168350 A281151 A337722

Adjacent sequences: A078590 A078591 A078592 * A078594 A078595 A078596

Keyword

nonn

Author

Benoit Cloitre, Dec 08 2002

Status

approved