A383833 Area of the unique primitive Pythagorean triple whose inradius is A000217(n) and such that its long leg and its hypotenuse are consecutive natural numbers.

0, 6, 84, 546, 2310, 7440, 19866, 46284, 97236, 188370, 341880, 588126, 967434, 1532076, 2348430, 3499320, 5086536, 7233534, 10088316, 13826490, 18654510, 24813096, 32580834, 42277956, 54270300, 68973450, 86857056, 108449334, 134341746, 165193860, 201738390

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 2025.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Miguel-Ángel Pérez García-Ortega, El Libro de las Ternas Pitagóricas.

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

a(n) = A000217(n) * (A000217(n) + 1) * (2*A000217(n) + 1).

From Andrew Howroyd, Nov 12 2025: (Start)

a(n) = n*(n + 1)*(n^2 + n + 1)*(n^2 + n + 2)/4.

G.f.: 6*x*(1 + 3*x + x^2)*(1 + 4*x + x^2)/(1 - x)^7. (End)

Example

For n=1, the short leg is A002061(1) = 3 and the long leg is A212135(2) = 4 so the area is then a(1) = (3 * 4 )/2 = 6.

Mathematica

a=Table[(n(n+1))/2, {n, 0, 30}]; Apply[Join, Map[{#(#+1)(2#+1)}&, a]]

Crossrefs

Cf. A000217, A002061, A058919, A383834, A336535.

Sequence in context: A288321 A155191 A211171 * A338405 A054605 A119576

Adjacent sequences: A383830 A383831 A383832 * A383834 A383835 A383836

Keyword

nonn,easy

Author

Miguel-Ángel Pérez García-Ortega, May 11 2025

Status

approved