A334511 Eventual period of a single cell in rule 9 cellular automaton in a cyclic universe of width n.

2, 2, 2, 2, 2, 9, 5, 12, 18, 5, 22, 12, 26, 14, 30, 16, 34, 18, 38, 20, 42, 22, 46, 24, 50, 26, 54, 28, 58, 30, 62, 32, 66, 34, 70, 36, 74, 38, 78, 40, 82, 42, 86, 44, 90, 46, 94, 48, 98, 50, 102, 52, 106, 54, 110, 56, 114, 58, 118, 60, 122, 62, 126, 64, 130

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

Crossrefs

Cf. A180001, A334496, A334499-A334515.

Formula

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

G.f.: x*(2 + 2*x - 2*x^2 - 2*x^3 + 7*x^5 + 3*x^6 - 4*x^7 + 10*x^8 - 10*x^9 - 9*x^10 + 14*x^11 - 5*x^13) / ((1 - x)^2*(1 + x)^2).

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

(End)

Conjecture: a(n) = (3 - (-1)^n)*n/2 for n > 10. - Stefano Spezia, Sep 11 2021

Extensions

More terms from Jinyuan Wang, May 09 2020