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

18,1

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.

Links

Table of n, a(n) for n=18..83.

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

Example

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.

Crossrefs

Cf. A203286, A115264.

Sequence in context: A053090 A264400 A365660 * A309512 A225367 A283479

Adjacent sequences: A381586 A381587 A381588 * A381590 A381592 A381593

Keyword

nonn,new

Author

R. J. Mathar, Mar 12 2025

Status

approved