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).

12, 30, 70, 40, 56, 176, 126, 208, 408, 198, 154, 234, 84, 90, 330, 260, 546, 1026, 476, 456, 736, 286, 418, 1218, 828, 1178, 2378, 1188, 800, 1160, 390, 340, 900, 570, 644, 1364, 714, 374, 494, 144, 132, 532, 442, 1044, 1924, 874, 918, 1518, 608, 1116, 3196

Offset

1,1

Comments

This sequence gives the perimeters 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 A024364.

Links

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

Index entries related to Pythagorean Triples

Formula

Empirically:

- T(n, 1) = A002939(n+1),

- T(n, (3^(n-1) + 1)/2) = A001542(n+1),

- T(n, 3^(n-1)) = A033586(n).

Example

The first rows are:
   12
   30, 70, 40
   56, 176, 126, 208, 408, 198, 154, 234, 84
T(1,1) corresponds to the perimeter of the triangle with sides 3, 4, 5; hence T(1, 1) = 3 + 4 + 5 = 12.

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] + t[3, 1])

Crossrefs

Cf. A001542, A002939, A024364, A033586, A321768, A321769, A321770.

Sequence in context: A064483 A375718 A365277 * A334791 A110019 A069486

Adjacent sequences: A322178 A322179 A322180 * A322182 A322183 A322184

Keyword

nonn,tabf

Author

Rémy Sigrist, Nov 30 2018

Status

approved