login
Area common to integer-sided isosceles triangles (x,x,y) and (x,x,z=y+2d), sorted on x > z/2, d being positive.
1

%I #11 Jan 14 2020 01:04:15

%S 12,60,120,168,420,420,360,1260,660,1848,1008,2640,2772,1092,3120,

%T 4680,1980,5460,1680,5148,9240,3432,2448,7140,11220,14280,8580,3420,

%U 15912,10032,15960,5460,20748,15708,23940,4620,13260,21840,25080,8160,23712

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

%C 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.

%C 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

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

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

%K easy,nonn

%O 1,1

%A _Lekraj Beedassy_, Aug 17 2006, Aug 20 2006