A334509 Eventual period of a single cell in rule 41 cellular automaton in a cyclic universe of width n.

2, 2, 2, 2, 15, 2, 28, 8, 36, 20, 44, 12, 52, 28, 60, 16, 68, 36, 76, 20, 84, 44, 92, 24, 100, 52, 108, 28, 116, 60, 124, 32, 132, 68, 140, 36, 148, 76, 156, 40, 164, 84, 172, 44, 180, 92, 188, 48, 196, 100, 204, 52, 212, 108, 220, 56, 228, 116, 236, 60, 244, 124

Offset

1,1

Comments

Bradley Klee computed a(1)-a(10).

References

Bradley Klee, Posting to Math Fun Mailing List, Apr 26 2020.

Links

Table of n, a(n) for n=1..62.

Wolfram Research, Rule 41 - Wolfram Atlas of Simple Programs

Formula

Conjectures from Colin Barker, May 09 2020: (Start)

G.f.: x*(2 + 2*x + 2*x^2 + 2*x^3 + 11*x^4 - 2*x^5 + 24*x^6 + 4*x^7 + 8*x^8 + 18*x^9 - 10*x^10 - 2*x^11 - 5*x^12 - 10*x^13) / ((1 - x)^2*(1 + x)^2*(1 + x^2)^2).

a(n) = 2*a(n-4) - a(n-8) for n > 14. (End)

Conjecture: a(n) = n*A176895(n) for n > 6. - Stefano Spezia, Oct 03 2021

Mathematica

Table[-Subtract @@ Flatten[Map[Position[#, #[[-1]]] &, NestWhileList[CellularAutomaton[41], Prepend[Table[0, {n - 1}], 1], Unequal, All], {0}]], {n, 62}] (* Stefano Spezia, Oct 04 2021, after Ben Branman in A180001 *)

Crossrefs

Cf. A176895, A180001, A334496, A334499-A334515.

Sequence in context: A084961 A226398 A248768 * A029643 A100687 A067096

Adjacent sequences: A334506 A334507 A334508 * A334510 A334511 A334512

Keyword

nonn

Author

N. J. A. Sloane, May 05 2020

Extensions

More terms from Jinyuan Wang, May 09 2020

Status

approved