A377726 Table read by rows: row n is the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 is A002315(n) and such that its long leg and its hypotenuse are consecutive natural numbers.

1, 0, 1, 13, 84, 85, 81, 3280, 3281, 477, 113764, 113765, 2785, 3878112, 3878113, 16237, 131820084, 131820085, 94641, 4478459440, 4478459441, 551613, 152138450884, 152138450885, 3215041, 5168244315840, 5168244315841, 18738637, 175568258308884, 175568258308885

Offset

1,4

Comments

row(1) = (1,0,1) is included by convention.

References

Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2024.

Links

Table of n, a(n) for n=1..30.

Formula

row(n) = (2*A002315(n) - 1, 2*A002315(n)(A002315(n) - 1), 2*A002315(n)(A002315(n) - 1) + 1).

Example

 n=1:      1,         0,         1;
 n=2:     13,        84,        85;
 n=3:     81,      3280,      3281;
 n=4:    477,    113764,    113765;

Mathematica

ra[n_]:=ra[n]=Module[{ra}, ra=((1+Sqrt[2])^(2n+1)-(Sqrt[2]-1)^(2n+1))/2; {2ra-1, 2ra^2-2ra, 2ra^2-2ra+1}]; exradio={}; Do[exradio=Join[exradio, FullSimplify[ra[n]]], {n, 0, 10}]; exradio

Crossrefs

Cf. A002315, A377011, A377016, A377017, A377725.

Sequence in context: A274398 A301953 A321589 * A225129 A297207 A222491

Adjacent sequences: A377723 A377724 A377725 * A377727 A377728 A377729

Keyword

nonn,easy,tabf

Author

Miguel-Ángel Pérez García-Ortega, Nov 05 2024

Status

approved