A386556 Number of 2-colorings of an 6 X 6 X 6 grid / cube, up to rotational symmetry, by the number of black cells.

1, 11, 1013, 69045, 3677374, 155822419, 5479820520, 164392285865, 4294750355129, 99256405950180, 2054607644379763, 38477196919023712, 657318781413490584, 10314848558604181280, 149565304110190970723, 2014146095209708440612, 25302710321203873065217, 297678944953786351579885, 3291006113657215317985320

Offset

0,2

Comments

This sequence is finite, having 6^3+1 terms. The cycle index Z(C) of the permutation group C of the rotations of the cube acting on the cells is given by 1/24 (a[1]^216 + 8 * a[1]^6 * a[3]^70 + 9 * a[2]^108 + 6 * a[4]^54).

References

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, 1973, page 35.

Links

Marko Riedel, Table of n, a(n) for n = 0..216

Formula

a(n) = [z^n] Z(C; 1+z).

Crossrefs

Cf. A334616, A386553, A386554, A386555.

Sequence in context: A015511 A065050 A099440 * A073903 A069710 A046187

Adjacent sequences: A386553 A386554 A386555 * A386557 A386558 A386559

Keyword

nonn,fini,full

Author

Marko Riedel, Jul 25 2025

Status

approved