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A367036 Number of distinct bracelets of length n (A000029) that eventually result in a cycle with length 2 or greater when used as the starting conditions for a rule 161 cellular automaton in a cyclic universe of circumference n.

0, 1, 0, 3, 6, 5, 0, 21, 41, 72, 123, 196, 263, 141, 18, 1440, 4096, 7653, 14251, 26900, 50771, 96743, 184329, 352548, 674886

Offset: 1

Angelo Rosso, Nov 02 2023

			For n = 2, the three bracelets are 00, 10, 11. Their progressions are as follows:
  00 -> 11 -> 11 -> 11 -> ...
  10 -> 01 -> 10 -> 01 -> ...
  11 -> 11 -> 11 -> 11 -> ...
a(2)=1 because only 01 eventually enters a cycle.

Cf. A000029, A334506.

a(21)-a(25) from Pontus von Brömssen, Nov 03 2023

A367054 Number of iterations until a repeating cycle begins in rule 161 cellular automaton in a cyclic universe of circumference n starting with one cell on.

Original entry on oeis.org

0, 0, 2, 0, 0, 4, 4, 0, 0, 2, 2, 0, 0, 8, 8, 0, 0, 2, 2, 0, 0, 4, 4, 0, 0, 2, 2, 0, 0, 16, 16, 0, 0, 2, 2, 0, 0, 4, 4, 0, 0, 2, 2, 0, 0, 8, 8, 0, 0, 2, 2, 0, 0, 4, 4, 0, 0, 2, 2, 0, 0, 32, 32, 0, 0, 2, 2, 0, 0, 4, 4, 0, 0, 2, 2, 0, 0, 8, 8, 0, 0, 2, 2, 0, 0, 4, 4, 0, 0, 2, 2

Offset: 1

Angelo Rosso, Nov 03 2023

nonn

			For n = 2 we have: 10 -> 01 -> 10; since the cycle started from the 0th iteration, a(2) = 0.
For n = 3 we have: 100 -> 000 -> 111 -> 111; since the cycle started from the 2nd iteration, a(3) = 2.

Cf. A334506, A000029.

A354464 Number of distinct bracelets of length n (A000029) that eventually result in a cycle with length 2 or greater when used as the starting conditions for a rule 18 cellular automaton in a cyclic universe of circumference n.

Original entry on oeis.org

0, 0, 0, 1, 4, 3, 0, 11, 35, 62, 108, 182, 273, 195, 17, 1131, 3976, 7464, 13970, 26413, 50049, 95638, 182763, 350249, 671304

Offset: 1

Angelo Rosso, Jul 27 2022

			For n = 4, the six bracelets are 0000, 1000, 1100, 1010, 1110, 1111. a(4)=1 because only 1100 eventually enters a cycle that is not 0000 -> 0000.

Cf. A000029.

Definition clarified and corrected by Angelo Rosso, Nov 02 2023
Term 2 corrected by Angelo Rosso, Nov 02 2023
a(21)-a(25) from Pontus von Brömssen, Nov 03 2023

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User: Angelo Rosso

A367036 Number of distinct bracelets of length n (A000029) that eventually result in a cycle with length 2 or greater when used as the starting conditions for a rule 161 cellular automaton in a cyclic universe of circumference n.

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A367054 Number of iterations until a repeating cycle begins in rule 161 cellular automaton in a cyclic universe of circumference n starting with one cell on.

Views

Author

Keywords

Examples

Crossrefs

A354464 Number of distinct bracelets of length n (A000029) that eventually result in a cycle with length 2 or greater when used as the starting conditions for a rule 18 cellular automaton in a cyclic universe of circumference n.

Views

Author

Keywords

Examples

Crossrefs

Extensions