cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A135622 #9 Jul 29 2025 14:28:55
%S A135622 3,15,48,35,63,128,63,135,243,240,320,99,231,275,495,384,576,768,143,
%T A135622 351,455,819,975,560,896,1008,1344,195,495,675,1215,735,1575,1875,768,
%U A135622 1280,1536,2048,2304,255,663,935,1683,1071,2295,2499,2975,1008,1728
%N A135622 16*Area^2 of integer triangles [A070080(n),A070081(n),A070082(n)].
%F A135622 a(n)=(u+v+w)*(-u+v+w)*(u-v+w)*(u+v-w), where u=A070080(n), v=A070081(n), w=A070082(n).
%F A135622 A070086(n) = round(sqrt(a(n))/4).
%e A135622 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.
%Y A135622 See the formula section for the relationships with A070080, A070081, A070082, A070086.
%Y A135622 Cf. A317182 (range of values), A331011 (nonunique values), A331250 (counts triangles by area).
%Y A135622 Cf. A316853 (with terms ordered as for A316841), and using this order for other sets of triangles: A046131, A055595, A070786.
%K A135622 nonn,easy
%O A135622 1,1
%A A135622 _Franz Vrabec_, Feb 29 2008