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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) / 2.
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%I #13 Dec 01 2018 12:20:49

%S 6,30,210,60,84,1320,630,1560,7140,1386,924,2340,210,180,4620,2730,

%T 10920,45144,7854,7980,23184,2574,5016,63336,26910,49476,242556,50490,

%U 25200,57420,4290,3570,34650,12540,14490,79794,18564,5610,10374,504,330,11970,7956

%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) / 2.

%C This sequence gives the areas 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 A024406.

%H Rémy Sigrist, <a href="/A322170/b322170.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) = A055112(n),

%F - T(n, (3^(n-1) + 1)/2) = A029549(n),

%F - T(n, 3^(n-1)) = A069072(n-1).

%e The first rows are:

%e 6

%e 30, 210, 60

%e 84, 1320, 630, 1560, 7140, 1386, 924, 2340, 210

%e T(1,1) corresponds to the area of the triangle with sides 3, 4, 5; hence T(1, 1) = 3 * 4 / 2 = 6.

%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] / 2)

%Y Cf. A024406, A029549, A055112, A069072, A321768, A321769.

%K nonn,tabf

%O 1,1

%A _Rémy Sigrist_, Nov 29 2018