A051585 Number of integer-sided triangles of area 6n.

1, 2, 0, 2, 1, 2, 1, 2, 1, 4, 1, 1, 0, 4, 2, 2, 0, 2, 1, 4, 3, 1, 0, 2, 1, 2, 0, 4, 0, 2, 0, 2, 1, 1, 6, 3, 0, 0, 1, 5, 0, 3, 0, 3, 2, 0, 0, 2, 1, 4, 1, 0, 0, 2, 4, 8, 0, 0, 0, 5, 0, 0, 1, 2, 1, 3, 0, 1, 0, 15, 0, 2, 0, 0, 0, 4, 2, 1, 0, 5, 1, 0, 0, 6, 2, 0, 1, 3, 0, 4, 3, 0, 0, 0, 1, 2, 0, 2, 1, 2, 0, 0, 0

Offset

1,2

Comments

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

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000

Prog

(PARI) a(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))) \\ Charles R Greathouse IV, Jun 27 2013

Crossrefs

Cf. A051584, A051586.

Sequence in context: A107455 A039701 A025822 * A049115 A294204 A329697

Adjacent sequences: A051582 A051583 A051584 * A051586 A051587 A051588

Keyword

nonn

Author

David W. Wilson

Status

approved