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

1,1

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

Links

Table of n, a(n) for n=1..41.

Formula

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

Example

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

Crossrefs

Sequence in context: A338159 A273691 A094807 * A099829 A099830 A361568

Adjacent sequences: A120641 A120642 A120643 * A120645 A120646 A120647

Keyword

easy,nonn

Author

Lekraj Beedassy, Aug 17 2006, Aug 20 2006

Status

approved