A380964 Number of 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

17,1

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

Links

Bert Dobbelaere, Table of n, a(n) for n = 17..100

R. J. Mathar, Generating Perimeter-magic Polygons (C++ source) (2025)

Example

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

Crossrefs

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

Sequence in context: A173895 A392338 A341757 * A286437 A212107 A073979

Adjacent sequences: A380961 A380962 A380963 * A380965 A380966 A380967

Keyword

nonn

Author

Derek Holton and Alex Holton, Feb 09 2025

Extensions

More terms from Bert Dobbelaere, Mar 15 2025

Status

approved