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%I #24 Dec 01 2018 05:01:25
%S 3,5,7,5,7,11,9,13,17,11,11,13,7,9,15,13,21,27,17,19,23,13,19,29,23,
%T 31,41,27,25,29,15,17,25,19,23,31,21,17,19,9,11,19,17,29,37,23,27,33,
%U 19,31,47,37,49,65,43,39,45,23,29,43,33,41,55,37,31,35,17
%N Triangle T(n, k) read by rows, n > 0 and 0 < k <= 3^(n-1): T(n, k) = sqrt(A321769(n, k) + A321770(n, k)).
%C This sequence and A321785 are related to a parametrization of the primitive Pythagorean triples in the tree described in A321768.
%H Rémy Sigrist, <a href="/A321784/b321784.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) = 2*n + 1,
%F - T(n, (3^(n-1) + 1)/2) = A001333(n+1),
%F - T(n, 3^(n-1)) = 2*n + 1.
%e The first rows are:
%e 3
%e 5, 7, 5
%e 7, 11, 9, 13, 17, 11, 11, 13, 7
%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[2, 1] + t[3, 1]))
%Y Cf. A001333, A321768, A321769, A321770, A321785.
%K nonn,tabf
%O 1,1
%A _Rémy Sigrist_, Nov 22 2018
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