A382455 Order 3 perimeter magic squares of magic sum n, all elements distinct and 1 in the set; bracelet symmetry.

3, 9, 23, 45, 75, 109, 178, 220, 324, 403, 545, 623, 872, 945, 1238, 1397, 1725, 1878, 2390, 2530, 3087, 3317, 3968, 4212, 5057, 5256, 6186, 6569, 7569, 7893, 9201, 9511, 10890, 11359, 12863, 13340, 15135, 15543, 17492, 18145, 20170, 20739, 23212, 23784, 26325, 27100, 29813, 30598, 33727

Offset: 12

Author

R. J. Mathar, Mar 26 2025

Keywords

• nonn

Comments

The order-3 perimeter-magic square has 3 positive integers (=order) per side (4 at corners, 4 within edges, total 8) where the sum of the 3 integers on each side is the same. Here we require that all 8 integers are distinct, that 1 is one of them, and that rotations and flips are not counted separately (recognizing the bracelet symmetry).

Links

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

Crossrefs

Cf. A380962 (1 not necessarily included), A084569 (elements not necess. distinct).

Formula

a(n) = A380962(n)-A380962(n-3).