A386555 Number of 2-colorings of an 5 X 5 X 5 grid, up to rotational symmetry, by the number of black cells.

1, 10, 355, 13375, 404775, 9775852, 195462780, 3322598660, 49007581605, 637095486150, 7390299421967, 77262191948715, 733990748643925, 6380073195502170, 51040584989484940, 377700327297519628, 2596689746386426870, 16649363658225874915, 99896181927621097005

Offset: 0

Author

Marko Riedel, Jul 25 2025

Keywords

• nonn
• fini
• full

Comments

This sequence is finite, having 5^3+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]^125 + 8 * a[1]^5 * a[3]^40 + 9 * a[1]^5 * a[2]^60 + 6 * a[1]^5 * a[4]^30).

References

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

Links

• Sean A. Irvine, Table of n, a(n) for n = 0..125

Crossrefs

Cf. A334616, A386553, A386554, A386556.

Formula

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