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

0,2

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.

Links

Table of n, a(n) for n=0..27.

Formula

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

Crossrefs

Cf. A334616, A386554, A386555, A386556.

Sequence in context: A283055 A394140 A097593 * A188686 A025756 A366119

Adjacent sequences: A386550 A386551 A386552 * A386554 A386555 A386556

Keyword

nonn,fini,full

Author

Marko Riedel, Jul 25 2025

Status

approved