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.

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

Offset

1,1

Comments

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.

Links

Rémy Sigrist, Rows n = 1..9, flattened

Index entries related to Pythagorean Triples

Formula

Empirically:

- T(n, 1) = A055112(n),

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

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

Example

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.

Prog

(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)

Crossrefs

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

Sequence in context: A370751 A325950 A275953 * A362375 A369959 A057896

Adjacent sequences: A322167 A322168 A322169 * A322171 A322172 A322173

Keyword

nonn,tabf

Author

Rémy Sigrist, Nov 29 2018

Status

approved