A384288 Length of the long leg in the unique primitive Pythagorean triple whose inradius is A002378(n) and such that its long leg and its hypotenuse are consecutive natural numbers.

12, 84, 312, 840, 1860, 3612, 6384, 10512, 16380, 24420, 35112, 48984, 66612, 88620, 115680, 148512, 187884, 234612, 289560, 353640, 427812, 513084, 610512, 721200, 846300, 987012, 1144584, 1320312, 1515540, 1731660, 1970112, 2232384, 2520012, 2834580

Offset: 1

Author

Miguel-Ángel Pérez García-Ortega, May 31 2025

Keywords

• nonn
• easy

Examples

			Triangles begin:
  n=1:      5,   12,   13;
  n=2:     13,   84,   85;
  n=3:     25,  312,  313;
  ...
This sequence gives the middle column.
		

Links

• José Miguel Blanco Casado and Miguel-Ángel Pérez García-Ortega, El Libro de las Ternas Pitagóricas

Crossrefs

Cf. A002378 (inradius), A001844 (short leg), A008514 (sum of the legs), A237516 (semiperimeter), A384566 (area).

Formula

a(n) = 2 * A002378(n) * (A002378(n) + 1).