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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.
1
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
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
KEYWORD
easy,nonn
AUTHOR
Lekraj Beedassy, Aug 17 2006, Aug 20 2006
STATUS
approved