A051584 Number of integer-sided triangles of area n.

0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 4

Offset

1,12

Comments

If integer-sided triangle has integer area, area is divisible by 6.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10085

Prog

(PARI)
A051585(n) = sum(z=sqrtint(sqrtint(192*n^2)-1)+1, sqrtint(9*(64*n^2+5)\20), sum(y=z\2+1, z, my(t=(y*z)^2-(12*n)^2, x); if(issquare(t, &t), (issquare(y^2+z^2-2*t, &x) && x<=y) + (t && issquare(y^2+z^2+2*t, &x) && x<=y), 0))); \\ From A051585 by Charles R Greathouse IV
A051584(n) = if((n%6), 0, A051585(n/6)); \\ Antti Karttunen, Aug 23 2019

Crossrefs

Cf. A051585, A051586.

Sequence in context: A028661 A028714 A028653 * A028645 A028710 A178926

Adjacent sequences: A051581 A051582 A051583 * A051585 A051586 A051587

Keyword

nonn

Author

David W. Wilson

Extensions

Data section extended up to a(120) by Antti Karttunen, Aug 23 2019

Status

approved