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%I #8 Nov 27 2016 22:02:55
%S 6,0,15,60,0,28,0,105,0,45,210,0,0,0,66,0,315,0,231,0,91,504,0,440,0,
%T 312,0,120,0,693,0,585,0,0,0,153,990,0,910,0,0,0,510,0,190,0,1287,0,
%U 1155,0,935,0,627,0,231,1716,0,0,0,1428,0,1140,0,0,0,276,0,2145,0,1989,0,1729,0,1365,0,897,0,325,2730,0,2618,0,2394,0,0,0,1610,0,1050,0,378,0,3315,0,3135,0,0,0,2415,0,0,0,0,0,435
%N Triangle T read by rows: T(n, m), for n >= 2, and m = 1, 2, ..., n-1, equals the square root of the positive integer solution y of y^2 = x^3 - A(n, m)^2*x with the area A(n, m) = A249869(n, m) of the primitive Pythagorean triangle characterized by (n, m) or 0 if no such triangle exists.
%C The corresponding solutions x are given in A278711, where also details are found.
%F T(n, m) = (n^2 - m^2)*n if n > m >= 1, gcd(n, m) = 1 and n+m is odd, and T(n, m) = 0 otherwise.
%e The triangle T(n, m) begins:
%e n\m 1 2 3 4 5 6 7 8 9 10
%e 2: 6
%e 3: 0 15
%e 4: 60 0 28
%e 5: 0 105 0 45
%e 6: 210 0 0 0 66
%e 7: 0 315 0 231 0 91
%e 8: 504 0 440 0 312 0 120
%e 9: 0 693 0 585 0 0 0 153
%e 10: 990 0 910 0 0 0 510 0 190
%e 11: 0 1287 0 1155 0 935 0 627 0 231
%e ...
%e n = 12: 1716 0 0 0 1428 0 1140 0 0 0 276,
%e n = 13: 0 2145 0 1989 0 1729 0 1365 0 897 0 325,
%e n = 14: 2730 0 2618 0 2394 0 0 0 1610 0 1050 0 378,
%e n = 15: 0 3315 0 3135 0 0 0 2415 0 0 0 0 0 435.
%e ...
%e For the solutions [x,y] see A278711.
%Y Cf. A278711.
%K nonn,tabl,easy
%O 2,1
%A _Wolfdieter Lang_, Nov 27 2016
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