A378966 Area of 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.

0, 546, 132840, 27132714, 5400270960, 1070181351954, 211922939930520, 41960773653737946, 8308058686721274720, 1644954930586205575554, 325692811387179035829960, 64485533166912548464047114, 12767809924078284782564882640, 2527961881127459862292727058546, 500523684710829430645198931758200

Offset

0,2

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=0..14.

Formula

a(n) = (A377726(n,1) * A377726(n,2))/2.

Example

For n=2, the short leg is A377726(2,1) = 13 and the long leg   so the semiperimeter is then a(2) = (13 * 84)/2 =546.

Mathematica

ar[n_]:=ar[n]= Module[{ra}, ra=((1+Sqrt[2])^(2n+1)-(Sqrt[2]-1)^(2n+1))/2; {ra(ra-1)(2ra-1)}]; areas={}; Do[areas=Join[areas, FullSimplify[ar[n]]], {n, 0, 16}]; areas

Crossrefs

Cf. A002315, A377011, A377016, A377017, A377726, A378965.

Sequence in context: A286440 A271448 A347203 * A176089 A261112 A219082

Adjacent sequences: A378963 A378964 A378965 * A378967 A378968 A378969

Keyword

nonn,easy,new

Author

Miguel-Ángel Pérez García-Ortega, Dec 12 2024

Status

approved