A384566 Area of the unique primitive Pythagorean triple whose inradius is A002378(n) and such that its long leg and its hypotenuse are consecutive natural numbers.

0, 30, 546, 3900, 17220, 56730, 153510, 360696, 762120, 1482390, 2698410, 4652340, 7665996, 12156690, 18654510, 27821040, 40469520, 57586446, 80354610, 110177580, 148705620, 197863050, 259877046, 337307880, 433080600, 550518150, 693375930, 865877796, 1072753500, 1319277570, 1611309630

Offset: 0

Author

Miguel-Ángel Pérez García-Ortega, Jun 03 2025

Keywords

• nonn
• easy

Comments

a(n) is multiple of 6 for all n.

Examples

			For n=1, the short leg is A384288(1,1) = 5 and the long leg is A384288(1,2) = 12 so the area is then a(1) = (5 * 12 )/2 = 30.
		

Links

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

Crossrefs

Cf. A002378, A384288, A008514, A237516.

Programs

Mathematica

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

Formula

a(n) = (A384288(n,1) * A384288(n,2))/2.

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