This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A120336 Number of solutions (x,y) of Diophantine equation y^2 = x*(a^N - x)*(b^N + x) (Weierstrass elliptic equation) with a and b legs in primitive Pythagorean triangles and N = 2. Sequence ordered in increasing values of leg "a". 0
 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Triads a = 3, b = 4, c = 5 and a = 4, b = 3, c = 5 provide different results for (x,y). LINKS EXAMPLE First primitive Pythagorean triad: 3, 4, 5. Weierstrass equation: y^2 = x*(3^2 - x)*(4^2 + x). Unique integer solution: (x,y) = (4,20). First element in the sequence: 1. Fifth primitive Pythagorean triad: 8, 15, 17. Integer solutions: (x,y) = (15, 420) and (30, 510). Fifth element in the sequence: 2. MAPLE # a, b, c primitive Pythagorean triad n_sol:=0; for x from 1 by 1 to a^2 do y2:= x*( a^2 - x)*( x+ b^2); if ((floor(sqrt(y2)))^2=y2) n_sol:=n_sol+1; fi; print(n_sol) ; od; CROSSREFS Cf. A009003, A020884, A120210, A120211, A120212, A120213. Sequence in context: A117456 A030621 A284582 * A284558 A294623 A039738 Adjacent sequences:  A120333 A120334 A120335 * A120337 A120338 A120339 KEYWORD nonn AUTHOR Giorgio Balzarotti and Paolo P. Lava, Jun 22 2006 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 23 03:00 EDT 2019. Contains 325230 sequences. (Running on oeis4.)