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 1-2 of 2 results.

A282817 Number of inequivalent ways to color the faces of a cube using at most n colors so that no color appears more than twice.

Original entry on oeis.org

0, 0, 0, 6, 72, 375, 1320, 3675, 8736, 18522, 36000, 65340, 112200, 184041, 290472, 443625, 658560, 953700, 1351296, 1877922, 2565000, 3449355, 4573800, 5987751, 7747872, 9918750, 12573600, 15795000, 19675656, 24319197, 29841000, 36369045, 44044800, 53024136
Offset: 0

Views

Author

David Nacin, Feb 21 2017

Keywords

Comments

Also the number of inequivalent ways to color the corners of an octahedron using at most n colors so that no color appears more than twice.

Examples

			For n=3 we get a(3)=6 ways to color the faces of a cube with three colors so that no color appears more than twice.
		

Crossrefs

Cf. A249460, A282816. A047780 (face colorings without restriction).

Programs

  • Mathematica
    Table[(3 n (n - 1) (n - 2)^2 + 6 n (n - 1) (n - 2) + n (n - 1) (n - 2) (n - 3) (n - 4) (n - 5) + 15 n (n - 1) (n - 2) (n - 3) (n - 4) + 45 n (n - 1) (n - 2) (n - 3) + 15 n (n - 1) (n - 2))/24, {n, 0, 16}]

Formula

a(n) = (n-2)^2*(n-1)*n^2*(n+5)/24.
G.f.: 3*x^3*(-2-10*x+x^2+x^3)/(x-1)^7 . - R. J. Mathar, Feb 23 2017

A282819 Number of inequivalent ways to color the edges of a tetrahedron using at most n colors so that no two opposite edges have the same color.

Original entry on oeis.org

0, 0, 2, 22, 152, 680, 2270, 6202, 14672, 31152, 60810, 110990, 191752, 316472, 502502, 771890, 1152160, 1677152, 2387922, 3333702, 4572920, 6174280, 8217902, 10796522, 14016752, 18000400, 22885850, 28829502, 36007272, 44616152, 54875830, 67030370, 81349952
Offset: 0

Views

Author

David Nacin, Feb 22 2017

Keywords

Examples

			For n = 2 we get a(2) = 2 distinct ways to color the edges of a tetrahedron in two colors so that no two opposite edges have the same color.
		

Crossrefs

Cf. A282816, A282818, A282820. A046023 (tetrahedral edge colorings without restriction).

Programs

  • Mathematica
    Table[(n - 1) n (n^4 - 2 n^3 + n^2 + 8)/12, {n, 0, 33}]
  • PARI
    a(n) = n*(n-1)*(n^4-2*n^3+n^2+8)/12 \\ Charles R Greathouse IV, Feb 22 2017

Formula

a(n) = n*(n-1)*(n^4-2*n^3+n^2+8)/12.
G.f.: -2*x^2*(1+4*x+20*x^2+4*x^3+x^4) / (x-1)^7 . - R. J. Mathar, Feb 23 2017
a(n) = 2*A282816(n). - R. J. Mathar, Feb 23 2017
Showing 1-2 of 2 results.