A120644 Area common to integer-sided isosceles triangles (x,x,y) and (x,x,z=y+2d), sorted on x > z/2, d being positive.

12, 60, 120, 168, 420, 420, 360, 1260, 660, 1848, 1008, 2640, 2772, 1092, 3120, 4680, 1980, 5460, 1680, 5148, 9240, 3432, 2448, 7140, 11220, 14280, 8580, 3420, 15912, 10032, 15960, 5460, 20748, 15708, 23940, 4620, 13260, 21840, 25080, 8160, 23712

Offset: 1

Author

Lekraj Beedassy, Aug 17 2006, Aug 20 2006

Keywords

• easy
• nonn

Comments

x=A020882(n); y=2*A046086(n); z=2*A046087(n); d=A120682(n). y is twice the height of the other triangle with z as base and conversely.

Take the n-th primitive Pythagorean triple (x, y, z) ordered by increasing z, then y. (1/x)^2 + (1/y)^2 = (z/w)^2, where a(n) = w. - Ivan N. Ianakiev, Jan 12 2020

Examples

			168 in the sequence refers to the area common to both triangle (25,25,14) and triangle (25,25,48).
		

Formula

a(n) = y*z/4 = A046086(n)*A046087(n) = 2*A120734(n).