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Triangle T(n, k) read by rows, n > 0 and 0 < k <= 3^(n-1): T(n, k) = A321768(n, k) + A321769(n, k) + A321770(n, k).
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%I #14 May 05 2020 01:19:18

%S 12,30,70,40,56,176,126,208,408,198,154,234,84,90,330,260,546,1026,

%T 476,456,736,286,418,1218,828,1178,2378,1188,800,1160,390,340,900,570,

%U 644,1364,714,374,494,144,132,532,442,1044,1924,874,918,1518,608,1116,3196

%N Triangle T(n, k) read by rows, n > 0 and 0 < k <= 3^(n-1): T(n, k) = A321768(n, k) + A321769(n, k) + A321770(n, k).

%C This sequence gives the perimeters of the primitive Pythagorean triangles corresponding to the primitive Pythagorean triples in the tree described in A321768.

%C If we order the terms in this sequence and keep duplicates then we obtain A024364.

%H Rémy Sigrist, <a href="/A322181/b322181.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) = A002939(n+1),

%F - T(n, (3^(n-1) + 1)/2) = A001542(n+1),

%F - T(n, 3^(n-1)) = A033586(n).

%e The first rows are:

%e 12

%e 30, 70, 40

%e 56, 176, 126, 208, 408, 198, 154, 234, 84

%e T(1,1) corresponds to the perimeter of the triangle with sides 3, 4, 5; hence T(1, 1) = 3 + 4 + 5 = 12.

%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 (t[1, 1] + t[2, 1] + t[3, 1])

%Y Cf. A001542, A002939, A024364, A033586, A321768, A321769, A321770.

%K nonn,tabf

%O 1,1

%A _Rémy Sigrist_, Nov 30 2018