A135622 16*Area^2 of integer triangles [A070080(n),A070081(n),A070082(n)].

3, 15, 48, 35, 63, 128, 63, 135, 243, 240, 320, 99, 231, 275, 495, 384, 576, 768, 143, 351, 455, 819, 975, 560, 896, 1008, 1344, 195, 495, 675, 1215, 735, 1575, 1875, 768, 1280, 1536, 2048, 2304, 255, 663, 935, 1683, 1071, 2295, 2499, 2975, 1008, 1728

Offset

1,1

Links

Table of n, a(n) for n=1..49.

Formula

a(n)=(u+v+w)*(-u+v+w)*(u-v+w)*(u+v-w), where u=A070080(n), v=A070081(n), w=A070082(n).

A070086(n) = round(sqrt(a(n))/4).

Example

A070080(4)=1, A070081(4)=3, A070082(4)=3, so a(4)=(1+3+3)*(-1+3+3)*(1-3+3)*(1+3-3)=35.

Crossrefs

See the formula section for the relationships with A070080, A070081, A070082, A070086.

Cf. A317182 (range of values), A331011 (nonunique values), A331250 (counts triangles by area).

Cf. A316853 (with terms ordered as for A316841), and using this order for other sets of triangles: A046131, A055595, A070786.

Sequence in context: A163383 A296799 A328111 * A316853 A061316 A124161

Adjacent sequences: A135619 A135620 A135621 * A135623 A135624 A135625

Keyword

nonn,easy

Author

Franz Vrabec, Feb 29 2008

Status

approved