A381589 The number of face-magic cubes with magic sum n and distinct positive integers at the vertices including 1.

3, 2, 6, 6, 16, 13, 21, 28, 38, 40, 57, 58, 81, 92, 108, 118, 150, 158, 188, 213, 242, 257, 309, 324, 373, 408, 448, 483, 551, 578, 643, 695, 759, 804, 894, 935, 1023, 1097, 1177, 1243, 1360, 1416, 1528, 1625, 1731, 1816, 1959, 2041, 2181, 2300, 2430, 2541, 2721, 2822, 2992, 3141, 3300, 3441, 3650, 3781, 3985, 4163, 4358, 4526, 4777, 4934

Offset: 18

Author

R. J. Mathar, Mar 12 2025

Keywords

• nonn

Comments

The face-magic cubes counted here have 8 distinct positive integers (including 1) at the vertices, and each sum over the 4 vertices of the 6 faces is the same. Cubes obtained by rotations or mirrors of the octahedral point group are counted only once.

Examples

			The 3 face-magic cubes with sum 18 are 1 4 5 8 - 6 7 2 3, 1 4 5 8 - 7 6 3 2 and 1 6 3 8 - 7 4 5 2, values at the base and values at the top face separated by a dash.
		

Links

• R. J. Mathar, Illustrations, conjectured g.f.

Crossrefs

Cf. A203286, A115264.