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.

Previous Showing 11-15 of 15 results.

A378476 The number of n-colorings of the vertices of the truncated dodecahedron up to rotation and reflection.

Original entry on oeis.org

0, 1, 9607679885269312, 353259652293727442874919719, 11076899964874301400431118585745408, 7228014483236696229750911410649667971875, 407280649839077145745380578110103790290896704, 4233515506163528044351709372473136729199352546645
Offset: 0

Views

Author

Peter Kagey, Nov 27 2024

Keywords

Comments

Equivalently,
1) the number of n-colorings of the faces of the triakis icosahedron, which is the polyhedral dual of the truncated dodecahedron.
2) the number of n-colorings of the faces of the pentakis dodecahedron, or n-colorings of the vertices of the truncated icosahedron, its polyhedral dual.
3) the number of n-colorings of the faces of the deltoidal hexecontahedron, or n-colorings of the vertices of the rhombicosidodecahedron, its polyhedral dual.
Colorings are counted up to the full icosahedral symmetry group of order 120.

Crossrefs

Formula

a(n) = (1/120)*(n^60 + 15*n^32 + 16*n^30 + 20*n^20 + 24*n^12 + 20*n^10 + 24*n^6).
Asymptotically, a(n) ~ n^60/120.

Extensions

a(0) = 0 prepended by Georg Fischer, Apr 16 2025

A378477 The number of n-colorings of the vertices of the truncated icosidodecahedron up to rotation and reflection.

Original entry on oeis.org

0, 1, 11076899964874299238703297447907328, 14975085832620260086776498590197757887552760437584786915, 14723725539819869413194145839524321308612931385268246121155792029614080, 6269303204385533375833261531851976948366440371233447120478861810030555725146484375
Offset: 0

Views

Author

Peter Kagey, Nov 27 2024

Keywords

Comments

Equivalently, the number of n-colorings of the faces of the disdyakis triacontahedron, which is the polyhedral dual of the truncated octahedron.
Colorings are counted up to the full icosahedral symmetry group of order 120.

Crossrefs

Formula

a(n) = 1/120*(n^120 + 31*n^60 + 20*n^40 + 24*n^24 + 20*n^20 + 24*n^12).
Asymptotically, a(n) ~ n^120/120

A378478 The number of n-colorings of the vertices of the snub dodecahedron up to rotation.

Original entry on oeis.org

0, 1, 19215358678900736, 706519304586988199183738259, 22153799929748598169960860333637632, 14456028966473392453665534687042333984375, 814561299678154291488767806377392301451223040, 8467031012327056088703142262372040966699399765293
Offset: 0

Views

Author

Peter Kagey, Nov 27 2024

Keywords

Comments

Equivalently, the number of n-colorings of the faces of the pentagonal hexecontahedron, which is the polyhedral dual of the snub dodecahedron.
Colorings are counted up to the rotational icosahedral symmetry group of order 60.

Crossrefs

Formula

a(n) = 1/60*(n^60 + 15*n^30 + 20*n^20 + 24*n^12).
Asymptotically, a(n) ~ n^60/60.

A333418 Irregular triangle: T(n,k) gives the number of ways to 2-color k edges of the n-cube up to rotation and reflection, with 0 <= k <= A001787(n).

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 1, 1, 4, 9, 18, 24, 30, 24, 18, 9, 4, 1, 1, 1, 1, 6, 24, 140, 604, 2596, 9143
Offset: 1

Views

Author

Peter Kagey, Mar 20 2020

Keywords

Comments

Conjecture: All rows are unimodal (increasing, then decreasing).
Each row is a palindrome.
A333333 is analogous with the restriction that the colorings must be connected.

Examples

			Table begins:
n\k| 0  1   2   3    4    5     6     7   8  9 10 11 12 ...
---+-------------------------------------------------------
  1| 1, 1;
  2| 1, 1,  2,  1,   1;
  3| 1, 1,  4,  9,  18,  24,   30,   24, 18, 9, 4, 1, 1;
  4| 1, 1,  6, 24, 140, 604, 2596, 9143, ...
  5| 1, 1,  8, 50, 608, ...
  6| 1, 1, 10, 89, ...
		

Crossrefs

Formula

T(n,k) >= ceiling(binomial(A001787(n),k)/A000165(n)).

A333444 Number of 2-colorings of edges of the n-cube up to isometry.

Original entry on oeis.org

2, 6, 144, 11251322, 314824456456819827136, 136221825854745676520058554256163406987047485113810944
Offset: 1

Views

Author

Peter Kagey, Mar 21 2020

Keywords

Comments

Bounded below by ceiling(2^A001787(n)/A000165(n)).

Crossrefs

Row sums of A333418.
Previous Showing 11-15 of 15 results.