OFFSET
1,1
COMMENTS
See Corolario 5.1.1. of the reference file (second section).
REFERENCES
J. M. Blanco Casado, J. M. Sánchez Muñoz, and M. A. Pérez García-Ortega, El Libro de las Ternas Pitagóricas, Preprint 2023.
LINKS
Miguel-Ángel Pérez García-Ortega, Capitulo 5. Catetos, El Libro de las Ternas Pitagóricas.
FORMULA
(a_1, b_1, c_1) = (3,4,5) and for each n > 1:
(a_n, b_n, c_n) = (a_(n-1)+b_(n-1), ((a_(n-1)+b_(n-1))^2-1)/2, ((a_(n-1)+b_(n-1))^2+1)/2)
EXAMPLE
Triples begin
3, 4, 5;
7, 24, 25;
31, 480, 481;
511, 130560, 130561;
...
MATHEMATICA
{a0, b0, c0}={3, 4, 5};
m=8;
f[n_]:=Module[{f0={a0, b0, c0}, f1={a0+b0, ((a0+b0)^2-1)/2, ((a0+b0)^2+1)/2}}, Do[{f0, f1}={f1, {Extract[f1, 1]+Extract[f1, 2], ((Extract[f1, 1]+Extract[f1, 2])^2-1)/2, ((Extract[f1, 1]+Extract[f1, 2])^2+1)/2}}, {n}]; f0]; t[n_]:={Extract[f[n], 1], Extract[f[n], 2], Extract[f[n], 3]};
ternas={a0, b0, c0}; For[i=1, i<=m, i++, ternas=Join[ternas, t[i]]];
ternas
CROSSREFS
KEYWORD
nonn,tabf,more
AUTHOR
Miguel-Ángel Pérez García-Ortega, Sep 20 2023
STATUS
approved