%I #20 Dec 01 2018 05:01:20

%S 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 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 17,17,5,19,19,9,23,23,9,13,13,3,19,19,13,29,29,13,23

%N 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 This sequence and A321784 are related to a parametrization of the primitive Pythagorean triples in the tree described in A321768.

%H Rémy Sigrist, <a href="/A321785/b321785.txt">Rows n = 1..9, flattened</a>

%H <a href="/index/Ps#PyTrip">Index entries related to Pythagorean Triples</a>

%F Empirically:

%F - T(n, 1) = 1,

%F - T(n, (3^(n-1) + 1)/2) = A001333(n),

%F - T(n, 3^(n-1)) = 2*n - 1.

%e The first rows are:

%e 1

%e 1, 3, 3

%e 1, 5, 5, 3, 7, 7, 3, 5, 5

%o (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 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 Cf. A001333, A321768, A321769, A321784.

%K nonn,tabf

%O 1,3

%A _Rémy Sigrist_, Nov 22 2018