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A322170
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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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2
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6, 30, 210, 60, 84, 1320, 630, 1560, 7140, 1386, 924, 2340, 210, 180, 4620, 2730, 10920, 45144, 7854, 7980, 23184, 2574, 5016, 63336, 26910, 49476, 242556, 50490, 25200, 57420, 4290, 3570, 34650, 12540, 14490, 79794, 18564, 5610, 10374, 504, 330, 11970, 7956
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OFFSET
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1,1
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COMMENTS
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This sequence gives the areas of the primitive Pythagorean triangles corresponding to the primitive Pythagorean triples in the tree described in A321768.
If we order the terms in this sequence and keep duplicates then we obtain A024406.
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LINKS
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FORMULA
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Empirically:
- T(n, (3^(n-1) + 1)/2) = A029549(n),
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EXAMPLE
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The first rows are:
6
30, 210, 60
84, 1320, 630, 1560, 7140, 1386, 924, 2340, 210
T(1,1) corresponds to the area of the triangle with sides 3, 4, 5; hence T(1, 1) = 3 * 4 / 2 = 6.
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PROG
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(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]];
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)
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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