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.

A249905 Smallest number of vertices supporting a graph with exactly n Hamiltonian cycles up to direction.

Original entry on oeis.org

2, 1, 5, 4, 5, 6, 5, 6, 6, 7, 6, 7, 5, 8, 6, 7, 6, 7, 6, 7, 7, 8, 7, 7, 6, 8, 7, 7, 7, 8, 7, 8, 7, 7, 7, 8, 6, 8, 7, 8, 7, 8, 8, 8, 8, 7, 8, 8, 7, 8, 8, 8, 7, 8, 8, 8, 8, 8, 8, 8, 6, 8, 7, 8, 8, 8, 8, 8, 8, 8, 7, 8, 7, 8, 8, 8, 7, 8, 8, 8, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9
Offset: 0

Views

Author

Jeremy Tan, Nov 08 2014

Keywords

Comments

"Up to direction" means that cycles differing only in starting vertex or direction of traversal are treated as one cycle. a(n) always exists since the wheel graph on n spokes has n cycles.

Examples

			a(3) = 4 since K_4 has 3 Hamiltonian cycles up to direction.

Links

Crossrefs

Cf. A244511 (a(n) <= 7), A249906 (records), A305190.

A244511 Possible numbers of Hamiltonian cycles up to direction in 7-vertex graphs.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24, 26, 27, 28, 30, 32, 33, 34, 36, 38, 40, 45, 48, 52, 60, 62, 70, 72, 76, 80, 90, 108, 120, 144, 168, 240, 360
Offset: 1

Views

Author

Jeremy Tan, Nov 11 2014

Keywords

Examples

			The empty graph on 7 vertices has no Hamiltonian cycles, so a(1) = 0. The cycle graph C_7 has exactly one so a(2) = 1.

Links

Crossrefs

Cf. A249905 (for the definition of "up to direction"), A249906, A253648 (numbers of Hamiltonian cycles that are not possible in 8-vertex graphs), A305190.

A253648 Numbers of Hamiltonian cycles that require a graph with at least 9 vertices.

Original entry on oeis.org

89, 91, 107, 117, 119, 121, 125, 127, 137, 141, 143, 151, 154, 155, 157, 159, 161, 163, 167, 170, 171, 173, 175, 178, 179, 181, 182, 185, 187, 189, 190, 191, 193, 195, 196, 197, 199, 201, 202, 203, 205, 206, 207, 209, 211, 213, 215, 217, 218, 221, 224, 225, 226, 227, 229, 233, 234, 235, 236, 237, 238, 239, 241, 242, 243, 244
Offset: 1

Views

Author

M. F. Hasler, Jan 18 2015

Keywords

Comments

Includes all numbers beyond 2520, starting from a(2290) = 2521 on, cf. formula. The first 2521 - 232 = 2289 terms contain the numbers in the interval [0, 2520] with 232 numbers missing, the largest being 2520.

Links

Crossrefs

Cf. A244511, A305190.

Formula

a(n) = n + 231 for n > 2289.
Showing 1-3 of 3 results.

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

Content is available under The OEIS End-User License Agreement.