A381589 - OEIS

%I #41 Mar 12 2025 11:02:36

%S 3,2,6,6,16,13,21,28,38,40,57,58,81,92,108,118,150,158,188,213,242,

%T 257,309,324,373,408,448,483,551,578,643,695,759,804,894,935,1023,

%U 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

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

%C 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.

%H R. J. Mathar, <a href="/A381589/a381589.pdf">Illustrations, conjectured g.f.</a>

%e 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.

%Y Cf. A203286, A115264.

%K nonn,new

%O 18,1

%A _R. J. Mathar_, Mar 12 2025