A380964 Perimeter-magic hexagons of order 3 with magic sum n.

9, 48, 150, 494, 1202, 2542, 4635, 9738, 14943, 25917, 41196, 62518, 89657, 139743, 185114, 264483, 363291, 485411, 630099, 862106, 1067459, 1391011, 1771817, 2210554, 2712337, 3461467, 4115434, 5073010, 6165577, 7387876, 8748214, 10655591, 12333486, 14679050, 17281206

Offset: 17

Author

Derek Holton and Alex Holton, Feb 09 2025

Keywords

• nonn

Comments

Each side of the hexagon has 3 integers (=the order), 2 of them shared by adjacent sides. All 12 integers on the vertices must be distinct. Solutions obtained by rotations around the 6-fold axis or flips are considered the same/equivalent (bracelet symmetry).

A244879(n-3) counts the perimeter-magic hexagons of order 3 if the 12 integers do not need to be distinct and if solutions by rotations/reflections are considered distinct. - R. J. Mathar, Mar 10 2025

Examples

			For magic sum 17, a(17) = 9. One of the hexagons is   5   9   3
                                                    10          8
                                                   2             6
                                                    14          7
                                                      1   12   4
		

Links

• Bert Dobbelaere, Table of n, a(n) for n = 17..100
• R. J. Mathar, Generating Perimeter-magic Polygons (C++ source) (2025)

Crossrefs

Cf. A380853 (triangles), A380962 (squares), A380963 (pentagons).

Extensions

More terms from Bert Dobbelaere, Mar 15 2025