%I #9 Apr 07 2024 05:31:42
%S 420,55440,23931600,142334216640,2137147184560080,
%T 4323341954766548553840,18705358317240372854759881380,
%U 1333577710124626249998068999458413600,248363720675646323338068819310182950300884320,4199805494977793853528867974891927438920668319491840
%N Areas of primitive Heron triangles with two rational medians from the infinite family based on Somos-5 sequences.
%H Andrew N. W. Hone, <a href="https://doi.org/10.1007/s40879-022-00586-w">Heron triangles with two rational medians and Somos-5 sequences</a>, European Journal of Mathematics, 8 (2022), 1424-1486; arXiv:<a href="https://arxiv.org/abs/2107.03197">2107.03197</a> [math.NT], 2021-2022.
%H Andrew N. W. Hone, <a href="https://doi.org/10.1007/s00283-024-10337-2">Heron Triangles and the Hunt for Unicorns</a>, Math. Intelligencer (2024); arXiv:<a href="https://arxiv.org/abs/2401.05581">2401.05581</a> [math.NT], 2024.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Heronian_triangle">Heronian triangle</a>
%F a(n) = |S(n)*S(n+1)*S(n+2)^2*S(n+3)*S(n+4)*T(n)*T(n+1)*T(n+2)^2*T(n+3)*T(n+4)|, where S(n) = A006721(n+2) and T(n) = A360381(n) [Hone, Eq. (1.21)].
%t t[1|3|4] = 1; t[2] = -1; t[5] = -7;
%t s[-2|-1|0|1|2] = 1;
%t Do[f[n_] := f[n] = (f[n-1] f[n-4] + f[n-2] f[n-3]) / f[n-5], {f, {t, s}}];
%t a[n_] := Abs@Product[f[n] f[n+1] f[n+2]^2 f[n+3] f[n+4], {f, {s, t}}];
%t Table[a[n], {n, 10}]
%Y Cf. A006721, A360381.
%Y This is a subsequence of A223941.
%K nonn
%O 1,1
%A _Andrey Zabolotskiy_, Feb 10 2023