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%I A322181 #14 May 05 2020 01:19:18
%S A322181 12,30,70,40,56,176,126,208,408,198,154,234,84,90,330,260,546,1026,
%T A322181 476,456,736,286,418,1218,828,1178,2378,1188,800,1160,390,340,900,570,
%U A322181 644,1364,714,374,494,144,132,532,442,1044,1924,874,918,1518,608,1116,3196
%N A322181 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 A322181 This sequence gives the perimeters of the primitive Pythagorean triangles corresponding to the primitive Pythagorean triples in the tree described in A321768.
%C A322181 If we order the terms in this sequence and keep duplicates then we obtain A024364.
%H A322181 Rémy Sigrist, <a href="/A322181/b322181.txt">Rows n = 1..9, flattened</a>
%H A322181 <a href="/index/Ps#PyTrip">Index entries related to Pythagorean Triples</a>
%F A322181 Empirically:
%F A322181 - T(n, 1) = A002939(n+1),
%F A322181 - T(n, (3^(n-1) + 1)/2) = A001542(n+1),
%F A322181 - T(n, 3^(n-1)) = A033586(n).
%e A322181 The first rows are:
%e A322181    12
%e A322181    30, 70, 40
%e A322181    56, 176, 126, 208, 408, 198, 154, 234, 84
%e A322181 T(1,1) corresponds to the perimeter of the triangle with sides 3, 4, 5; hence T(1, 1) = 3 + 4 + 5 = 12.
%o A322181 (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 A322181 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 A322181 Cf. A001542, A002939, A024364, A033586, A321768, A321769, A321770.
%K A322181 nonn,tabf
%O A322181 1,1
%A A322181 _Rémy Sigrist_, Nov 30 2018

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