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

Author

N. J. A. Sloane, May 05 2020

Keywords

• nonn

Comments

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

References

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

Links

• Wolfram Research, Rule 41 - Wolfram Atlas of Simple Programs

Crossrefs

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

Programs

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 *)

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

Extensions

More terms from Jinyuan Wang, May 09 2020