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

Author

Rémy Sigrist, Nov 30 2018

Keywords

• nonn
• tabf

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.

Examples

			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.
		

Links

• Rémy Sigrist, Rows n = 1..9, flattened
• Index entries related to Pythagorean Triples

Crossrefs

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

Programs

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])

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).