A382608 Long leg of the unique primitive Pythagorean triple whose inradius is A000045(n) and such that its long leg and its hypotenuse are consecutive natural numbers.

4, 4, 12, 24, 60, 144, 364, 924, 2380, 6160, 16020, 41760, 109044, 285012, 745420, 1950312, 5104012, 13359280, 34969884, 91543980, 239651724, 627394464, 1642504612, 4300075584, 11257651300, 29472763684, 77160454284, 202008299064, 528863957340, 1384582787280

Offset: 1

Author

Miguel-Ángel Pérez García-Ortega, Mar 31 2025

Keywords

• nonn
• easy

Examples

			Triangle begins:
  n=1:      3,    4,    5;
  n=2:      3,    4,    5;
  n=3:      5,   12,   13;
where this sequence is the middle column.
		

Links

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

Crossrefs

Cf. A000045 (inradius), A001588 (short leg), A382609 (semiperimeter), A382610 (area).

Programs

Mathematica

a=Table[Fibonacci[n],{n,0,16}];Apply[Join,Map[{2#+1,2#^2+2#,2#^2+2#+1}&,a]]

Formula

a(n) = 2*F(n)*(F(n) + 1) where F(n) = A000045(n).