A391073 a(n) is the number of nondegenerate triangles (n, n + d, n + 2*d) with integer area for some nonnegative integers d.

0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 3, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 3, 0, 0, 1, 1, 0, 1, 0, 0, 4, 0, 0, 1, 0, 0, 3, 0, 0, 1, 0, 1, 4, 1, 0, 1, 0, 0, 1, 1, 0, 3, 1, 0, 1, 0, 3, 1, 0, 1, 1, 0, 0, 1, 1, 0, 6, 0, 0, 4, 0, 0, 1, 0, 0, 1, 2, 0, 3

Offset

0,16

Comments

d < n because n + 2*d < n + (n + d).

Links

Felix Huber, Table of n, a(n) for n = 0..10000

Example

The a(15) = 3 triangles are (15, 20, 25) with d = 5 and area 150, (15, 26, 37) with d = 11 and area 156, (15, 28, 41) with d = 13 and area 126.

Maple

A391073 := proc(n) local b, c, d, x; c := 0; for d to n - 1 do x := 3*(n + d)^2*(n + 3*d)*(n - d); if irem(x, 16) = 0 then x := 1/16*x; b := isqrt(x); if b*b = x then c := c + 1; end if; end if; end do; c; end proc: seq(A391073(n), n = 1 .. 88);

Crossrefs

Cf. A024164, A336750, A351178, A379663, A387908.

Sequence in context: A307808 A200472 A397133 * A309887 A395033 A317595

Adjacent sequences: A391070 A391071 A391072 * A391074 A391075 A391076

Keyword

nonn

Author

Felix Huber, Dec 09 2025

Status

approved