A100686 a(1) = 1, a(2) = 2; thereafter a(2n+1) = |a(2n)^2-a(2n-1)^2|, a(2n+2) = 2*a(2n-1)*a(2n).

1, 2, 3, 4, 7, 24, 527, 336, 164833, 354144, 98248054847, 116749235904, 3977703802948722503807, 22940770664883067253376, 510456831154766758152181998159655209453904127, 182503181432559739767250904458105698387204864

Offset

1,2

Comments

s = 1 and t = 2 are the initial seed numbers; they give the first Pythagorean pair x = 3, y = 4. Then take s = x, t = y for next seed numbers; these give the next Pythagorean pair x = |s^2-t^2|, y = 2st. Then take s = x, t = y and so on.

Links

Table of n, a(n) for n=1..16.

Planet Math, Pythagorean Triplet

Example

a(9) = 527^2-336^2 = 164833 because a(7) = 527 and a(8) = 336.

Crossrefs

Sequence in context: A084644 A208729 A270777 * A052340 A370407 A094313

Adjacent sequences: A100683 A100684 A100685 * A100687 A100688 A100689

Keyword

nonn,easy

Author

Pahikkala Jussi, Dec 08 2004

Extensions

Edited by N. J. A. Sloane, Sep 06 2008

Defined a(2n+1) by absolute values, added 4 values - R. J. Mathar, Oct 14 2010

Status

approved