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 1-4 of 4 results.

A357620 Length of longest induced cycle (or chordless cycle) in the n-Fibonacci cube graph.

Original entry on oeis.org

0, 0, 0, 4, 4, 10, 14, 18, 30, 46
Offset: 0

Views

Author

Pontus von Brömssen, Oct 06 2022

Keywords

Links

Crossrefs

Cf. A000937, A297668, A357619.

Formula

a(n) <= A357619(n) + 2.

Extensions

a(9) from Elijah Beregovsky, Dec 03 2022

A358355 Maximum length of an induced path (or chordless path) in the n-halved cube graph.

Original entry on oeis.org

0, 1, 1, 2, 3, 6, 11, 18
Offset: 1

Views

Author

Pontus von Brömssen, Nov 12 2022

Keywords

Links

Crossrefs

Cf. A099155, A357619, A358356, A358357.

Formula

a(n) >= A358356(n) - 2.

A358357 Maximum length of an induced path (or chordless path) in the n-folded cube graph.

Original entry on oeis.org

1, 1, 2, 4, 10, 22
Offset: 2

Views

Author

Pontus von Brömssen, Nov 12 2022

Keywords

Links

Crossrefs

Cf. A099155, A357619, A358355, A358358.

Formula

a(n) >= A358358(n)-2. Equality holds for 3 <= n <= 7.
For n > 2, a(n) <= (2^(n-2)*n-1)/(n-1)-1. - Elijah Beregovsky, Dec 22 2022

A360362 Maximum number of moves required to reach an already visited color configuration, when applying the move described in A360360 to a deck of n colored cards.

Original entry on oeis.org

1, 2, 3, 6, 9, 13, 20, 30, 46, 74, 106, 152, 242, 318
Offset: 1

Views

Author

Pontus von Brömssen, Feb 04 2023

Keywords

Examples

			For n = 5, the initial configuration 01102 (with the top of the deck to the left) requires 9 moves to reach an already visited configuration: 01102 -> 11020 -> 10120 -> 01210 -> 12100 -> 21010 -> 12010 -> 20101 -> 02101 -> 21010. This is the maximum for 5 cards, so a(5) = 9.
Lexicographically first optimal initial configuration for 1 <= n <= 14:
   n  a(n)  configuration
   1    1   0
   2    2   01
   3    3   001
   4    6   0012
   5    9   01102
   6   13   010012
   7   20   0111023
   8   30   01232213
   9   46   012110234
  10   74   0111234234
  11  106   01112343324
  12  152   011102345345
  13  242   0122112345345
  14  318   01112345326546

Crossrefs

Cf. A357619, A360360, A360361.

Formula

a(n) = A357619(n) for 1 <= n <= 8, but it seems unlikely that this holds for all n.
a(n) <= A360360(n) + A360361(n). Equality holds (i.e., the maximum period and the maximum preperiod can be obtained with the same initial configuration) for n = 1, 2, 3, 4, 10, 12, 14, ... .
Showing 1-4 of 4 results.

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

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