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 1-8 of 8 results.

A343211 Number of (undirected) Hamiltonian cycles of the graph of the n-th Johnson solid.

Original entry on oeis.org

4, 5, 7, 11, 16, 90, 6, 16, 30, 80, 240, 6, 30, 12, 52, 160, 268, 67, 225, 716, 3550, 794, 6228, 44092, 194620, 9, 96, 396, 361, 1350, 1296, 6560, 6520, 32560, 708, 718, 6033, 45625, 45856, 221970, 221680, 1083340, 1082370, 8422, 162301, 2751301, 12817980
Offset: 1

Views

Author

Pontus von Brömssen, Apr 08 2021

Keywords

Examples

			The gyrobifastigium (J26) has a(26) = 9 Hamiltonian cycles.

Links

Crossrefs

Cf. A242731, A268283.

A358999 Number of undirected cycles of the Platonic graphs (in the order of tetrahedral, cubical, octahedral, dodecahedral, and icosahedral graph).

Original entry on oeis.org

7, 28, 63, 1168, 12878
Offset: 1

Views

Author

Seiichi Manyama, Dec 10 2022

Keywords

Examples

			   graph \ n-cycle   |  3  4  5   6   7    8    9   10   11   12 13 ...
  -------------------+-------------------------------------------------
   tetrahedral graph |  4  3
       cubical graph |  0  6  0  16   0    6
    octahedral graph |  8 15 24  16
  dodecahedral graph |  0  0 12   0   0   30   20   36  120  100 60 ...
   icosahedral graph | 20 30 72 240 720 1620 2680 3336 2880 1280

Links

Crossrefs

Cf. A053016, A268283, A359000, A359001, A359002.

A359000 Number of undirected n-cycles of the octahedral graph.

Original entry on oeis.org

8, 15, 24, 16
Offset: 3

Views

Author

Seiichi Manyama, Dec 10 2022

Keywords

Comments

a(3) = 8 = A053016(3).
a(6) = 16 = A268283(3)/2.

Links

Crossrefs

Cf. A053016, A268283, A358999, A359001, A359002.

A359001 Number of undirected n-cycles of the dodecahedral graph.

Original entry on oeis.org

12, 0, 0, 30, 20, 36, 120, 100, 60, 180, 180, 90, 180, 130, 0, 30
Offset: 5

Views

Author

Seiichi Manyama, Dec 10 2022

Keywords

Comments

a(5) = 12 = A053016(4).
a(20) = 30 = A268283(4)/2.

Links

Crossrefs

Cf. A053016, A268283, A358999, A359000, A359002.

A359002 Number of undirected n-cycles of the icosahedral graph.

Original entry on oeis.org

20, 30, 72, 240, 720, 1620, 2680, 3336, 2880, 1280
Offset: 3

Views

Author

Seiichi Manyama, Dec 10 2022

Keywords

Comments

a(3) = 20 = A053016(5).
a(12) = 1280 = A268283(5)/2.

Links

Crossrefs

Cf. A053016, A268283, A358999, A359000, A359001.

A343433 Sorted numbers of (undirected) Hamiltonian cycles in the graphs of the Archimedean solids.

Original entry on oeis.org

3, 6, 30, 44, 100, 1090, 1342, 6020, 39040, 845340, 47629064, 1446402032, 288087704535697
Offset: 1

Views

Author

Pontus von Brömssen, Apr 15 2021

Keywords

Examples

			The solids are in order:
  truncated tetrahedron (3),
  truncated cube (6),
  truncated dodecahedron (30),
  truncated octahedron (44),
  cuboctahedron (100),
  truncated icosahedron (1090),
  truncated cuboctahedron (1342),
  rhombicuboctahedron (6020),
  icosidodecahedron (39040),
  snub cube (845340),
  truncated icosidodecahedron (47629064),
  rhombicosidodecahedron (1446402032),
  snub dodecahedron (288087704535697).

Crossrefs

Cf. A268283, A343211, A343432, A343434.

A343434 Sorted numbers of (undirected) Hamiltonian cycles in the graphs of the Catalan solids (the Archimedean duals).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 6, 726, 1704, 348912, 1919220, 1685220540, 310880892720
Offset: 1

Views

Author

Pontus von Brömssen, Apr 19 2021

Keywords

Examples

			Six of the Catalan solids are not Hamiltonian, so a(n) = 0 for n <= 6. These solids are: the rhombic dodecahedron, the triakis octahedron, the deltoidal icositetrahedron, the rhombic triacontahedron, the triakis icosahedron, and the deltoidal hexecontahedron.
The remaining (Hamiltonian) solids are in order:
  triakis tetrahedron (6),
  pentagonal icositetrahedron (726),
  tetrakis hexahedron (1704),
  disdyakis dodecahedron (348912),
  pentagonal hexecontahedron (1919220),
  pentakis dodecahedron (1685220540),
  disdyakis triacontahedron (310880892720).

Crossrefs

Cf. A268283, A343211, A343433.

A358960 Number of directed Hamiltonian paths of the Platonic graphs (in the order of tetrahedral, cubical, octahedral, dodecahedral, and icosahedral graph).

Original entry on oeis.org

24, 144, 240, 3240, 75840
Offset: 1

Views

Author

Seiichi Manyama, Dec 07 2022

Keywords

Comments

a(n)/2 is the number of undirected Hamiltonian paths of the Platonic graph corresponding to a(n).
From symmetry, a(n) is a multiple of A063723(n).

Links

Crossrefs

Cf. A053016, A063723, A268283, A343213.
Showing 1-8 of 8 results.

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

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