A386553 Number of 2-colorings of an 3 X 3 X 3 grid, up to rotational symmetry, by the number of black cells.

1, 4, 22, 139, 779, 3455, 12507, 37303, 92968, 195963, 352433, 544382, 725612, 837184, 837184, 725612, 544382, 352433, 195963, 92968, 37303, 12507, 3455, 779, 139, 22, 4, 1

Offset: 0

Author

Marko Riedel, Jul 25 2025

Keywords

• nonn
• fini
• full

Comments

This sequence is finite, having 3^3+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]^27 + 8 * a[1]^3 * a[3]^8 + 9 * a[1]^3 * a[2]^12 + 6 * a[1]^3*a[4]^6).

References

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

Crossrefs

Cf. A334616, A386554, A386555, A386556.

Formula

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