A360537 Areas of primitive Heron triangles with two rational medians from the infinite family based on Somos-5 sequences.
420, 55440, 23931600, 142334216640, 2137147184560080, 4323341954766548553840, 18705358317240372854759881380, 1333577710124626249998068999458413600, 248363720675646323338068819310182950300884320, 4199805494977793853528867974891927438920668319491840
Offset: 1
Keywords
Links
- Andrew N. W. Hone, Heron triangles with two rational medians and Somos-5 sequences, European Journal of Mathematics, 8 (2022), 1424-1486; arXiv:2107.03197 [math.NT], 2021-2022.
- Andrew N. W. Hone, Heron Triangles and the Hunt for Unicorns, Math. Intelligencer (2024); arXiv:2401.05581 [math.NT], 2024.
- Wikipedia, Heronian triangle
Programs
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Mathematica
t[1|3|4] = 1; t[2] = -1; t[5] = -7; s[-2|-1|0|1|2] = 1; Do[f[n_] := f[n] = (f[n-1] f[n-4] + f[n-2] f[n-3]) / f[n-5], {f, {t, s}}]; a[n_] := Abs@Product[f[n] f[n+1] f[n+2]^2 f[n+3] f[n+4], {f, {s, t}}]; Table[a[n], {n, 10}]