%I A120336
%S A120336 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,
%T A120336 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,
%U A120336 1,1,1,1,2,1,1,1
%N 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".
%C A120336 Triads a = 3 b = 4 c = 5 and a = 4 b = 3 c = 5 provide different results 
               for (x,y).
%e A120336 First primitive Pythagorean triad: 3, 4, 5
%e A120336 Weierstrass equation. y^2 = x*( 3^2 -x)*( 4^2 + x)
%e A120336 Unique integer solution (x,y) = (4,20)
%e A120336 First element in the sequence = 1
%e A120336 Fifth primitive Pythagorean triad: 8, 15, 17
%e A120336 Integer solutions (x,y) = (15, 420) and (30, 510)
%e A120336 Fifth element in the sequence = 2
%p A120336 # 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;
%Y A120336 Cf. A009003, A020884, A120210, A120211, A120212, A120213.
%Y A120336 Sequence in context: A165633 A117456 A030621 this_sequence A039738 A075774 
               A078572
%Y A120336 Adjacent sequences: A120333 A120334 A120335 this_sequence A120337 A120338 
               A120339
%K A120336 nonn
%O A120336 1,5
%A A120336 Giorgio Balzarotti and Paolo P. Lava (greenblue(AT)tiscali.it), Jun 22 
               2006