A380105 Perimeter-magic triangles of order 3 with magic sum n, bracelet symmetry, and minimum term 1.

1, 3, 5, 12, 11, 20, 24, 33, 33, 52, 51, 68, 70, 90, 93, 117, 115, 143, 147, 175, 174, 210, 210, 245, 248, 285, 287, 330, 328, 375, 378, 423, 423, 477, 478, 530, 532, 588, 590, 652, 649, 713, 717, 780, 781, 852, 852, 923, 925, 1000, 1001, 1080, 1078, 1160, 1165, 1245, 1245, 1335, 1335

Offset: 9

Author

R. J. Mathar, Mar 11 2025

Keywords

• nonn

Comments

The setup is similar to A380853: triangles with 3 positive integers per side, all 6 values distinct, each side's sum equal to n, respecting the bracelet symmetry (rotations and flips generate equivalent triangles). But here 1 must be present at least once among the 6 values. The formula reflects that one can generate magic triangles where 1 is no longer present by adding 1 to each of the 6 integers, which increases the magic sum by 3.

Links

• R. J. Mathar, Generating perimeter-magic polygons, C++ (2025)

Crossrefs

Cf. A380853 (perimeter-magic triangles).

Formula

a(n) = A380853(n)-A380853(n-3).

G.f.: A380853(x)*(1-x^3).