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%I A322170 #13 Dec 01 2018 12:20:49
%S A322170 6,30,210,60,84,1320,630,1560,7140,1386,924,2340,210,180,4620,2730,
%T A322170 10920,45144,7854,7980,23184,2574,5016,63336,26910,49476,242556,50490,
%U A322170 25200,57420,4290,3570,34650,12540,14490,79794,18564,5610,10374,504,330,11970,7956
%N A322170 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 A322170 This sequence gives the areas of the primitive Pythagorean triangles corresponding to the primitive Pythagorean triples in the tree described in A321768.
%C A322170 If we order the terms in this sequence and keep duplicates then we obtain A024406.
%H A322170 Rémy Sigrist, <a href="/A322170/b322170.txt">Rows n = 1..9, flattened</a>
%H A322170 <a href="/index/Ps#PyTrip">Index entries related to Pythagorean Triples</a>
%F A322170 Empirically:
%F A322170 - T(n, 1) = A055112(n),
%F A322170 - T(n, (3^(n-1) + 1)/2) = A029549(n),
%F A322170 - T(n, 3^(n-1)) = A069072(n-1).
%e A322170 The first rows are:
%e A322170    6
%e A322170    30, 210, 60
%e A322170    84, 1320, 630, 1560, 7140, 1386, 924, 2340, 210
%e A322170 T(1,1) corresponds to the area of the triangle with sides 3, 4, 5; hence T(1, 1) = 3 * 4 / 2 = 6.
%o A322170 (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 A322170 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 A322170 Cf. A024406, A029549, A055112, A069072, A321768, A321769.
%K A322170 nonn,tabf
%O A322170 1,1
%A A322170 _Rémy Sigrist_, Nov 29 2018

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