cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A386554 Number of 2-colorings of an 4 X 4 X 4 grid, up to rotational symmetry, by the number of black cells.

Original entry on oeis.org

1, 4, 98, 1744, 26691, 317728, 3125882, 25884268, 184437452, 1147524988, 6311461050, 30983159856, 136842622391, 547369124016, 1993988770170, 6646625005908, 20355293012087, 57473757334488, 150070376844312, 363328255291128, 817488598547832, 1712833203324840
Offset: 0

Views

Author

Marko Riedel, Jul 25 2025

Keywords

Comments

This sequence is finite, having 4^3+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]^64 + 8 * a[1]^4 * a[3]^20 + 9 * a[2]^32 + 6 * a[4]^16).

References

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

Links

Crossrefs

Cf. A334616, A386553, A386555, A386556.

Formula

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

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

Original entry on oeis.org

1, 10, 355, 13375, 404775, 9775852, 195462780, 3322598660, 49007581605, 637095486150, 7390299421967, 77262191948715, 733990748643925, 6380073195502170, 51040584989484940, 377700327297519628, 2596689746386426870, 16649363658225874915, 99896181927621097005
Offset: 0

Views

Author

Marko Riedel, Jul 25 2025

Keywords

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

Crossrefs

Cf. A334616, A386553, A386554, A386556.

Formula

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

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

Original entry on oeis.org

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

Views

Author

Marko Riedel, Jul 25 2025

Keywords

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).
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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