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A321785 Triangle T(n, k) read by rows, n > 0 and 0 < k <= 3^(n-1): T(n, k) = sqrt(A321769(n, k)^2 - A321768(n, k)^2).

%I A321785 #20 Dec 01 2018 05:01:20
%S A321785 1,1,3,3,1,5,5,3,7,7,3,5,5,1,7,7,5,11,11,5,9,9,3,13,13,7,17,17,7,11,
%T A321785 11,3,11,11,5,13,13,5,7,7,1,9,9,7,15,15,7,13,13,5,21,21,11,27,27,11,
%U A321785 17,17,5,19,19,9,23,23,9,13,13,3,19,19,13,29,29,13,23
%N A321785 Triangle T(n, k) read by rows, n > 0 and 0 < k <= 3^(n-1): T(n, k) = sqrt(A321769(n, k)^2 - A321768(n, k)^2).
%C A321785 This sequence and A321784 are related to a parametrization of the primitive Pythagorean triples in the tree described in A321768.
%H A321785 Rémy Sigrist, <a href="/A321785/b321785.txt">Rows n = 1..9, flattened</a>
%H A321785 <a href="/index/Ps#PyTrip">Index entries related to Pythagorean Triples</a>
%F A321785 Empirically:
%F A321785 - T(n, 1) = 1,
%F A321785 - T(n, (3^(n-1) + 1)/2) = A001333(n),
%F A321785 - T(n, 3^(n-1)) = 2*n - 1.
%e A321785 The first rows are:
%e A321785    1
%e A321785    1, 3, 3
%e A321785    1, 5, 5, 3, 7, 7, 3, 5, 5
%o A321785 (PARI) M = [[1, -2, 2; 2, -1, 2; 2, -2, 3], [1, 2, 2; 2, 1, 2; 2, 2, 3], [-1, 2, 2; -2, 1, 2; -2, 2, 3]];
%o A321785 T(n, k) = my (t=[3; 4; 5], d=digits(3^(n-1)+k-1, 3)); for (i=2, #d, t = M[d[i]+1] * t); return (sqrtint(t[3, 1] - t[2, 1]))
%Y A321785 Cf. A001333, A321768, A321769, A321784.
%K A321785 nonn,tabf
%O A321785 1,3
%A A321785 _Rémy Sigrist_, Nov 22 2018