A334506 -id:A334506 - cp's OEIS frontend

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.

cp's OEIS Frontend

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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