A380964 -id:A380964 - cp's OEIS frontend

A380963 The number of perimeter-magic pentagons of order 3 with magic sum n.

1, 9, 33, 75, 233, 374, 742, 1294, 2042, 3029, 4931, 6535, 9507, 13214, 17577, 22762, 31335, 38341, 49660, 62791, 77689, 94239, 119151, 139727, 170553, 204832, 242122, 282811, 340914, 388834, 456668, 530819, 609982, 694982, 810204, 906951, 1038672

Offset: 14

Derek Holton and Alex Holton, Feb 09 2025

nonn

The requirements are that there are 3 integers at each side of the pentagon (2 of them shared by adjacent sides), which sum up to n. All 10 integers on the 5 sides must be distinct. Pentagons obtained by reflections or rotations are considered to be the same.

If the 10 integers do not need to be distinct and if solutions by rotations around the five-fold symmetry axis and flips are considered distinct, there are A244497(n-3) perimeter-magic pentagons. - R. J. Mathar, Mar 10 2025

			for n = 14, a(14) = 1           5
                              6    7
                            3         2
                             10      8
                              1  9  4

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

Cf. A380962 (perimeter-magic squares), A380853 (perimeter-magic triangles), A380964 (perimeter-magic hexagons).

cp's OEIS Frontend

A380963 The number of perimeter-magic pentagons of order 3 with magic sum n.

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