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%I #41 Oct 21 2021 01:46:51
%S 2,2,2,2,15,2,28,8,36,20,44,12,52,28,60,16,68,36,76,20,84,44,92,24,
%T 100,52,108,28,116,60,124,32,132,68,140,36,148,76,156,40,164,84,172,
%U 44,180,92,188,48,196,100,204,52,212,108,220,56,228,116,236,60,244,124
%N Eventual period of a single cell in rule 41 cellular automaton in a cyclic universe of width n.
%C _Bradley Klee_ computed a(1)-a(10).
%D Bradley Klee, Posting to Math Fun Mailing List, Apr 26 2020.
%H Wolfram Research, <a href="http://atlas.wolfram.com/01/01/41/">Rule 41 - Wolfram Atlas of Simple Programs</a>
%F Conjectures from _Colin Barker_, May 09 2020: (Start)
%F 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).
%F a(n) = 2*a(n-4) - a(n-8) for n > 14. (End)
%F Conjecture: a(n) = n*A176895(n) for n > 6. - _Stefano Spezia_, Oct 03 2021
%t 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 *)
%Y Cf. A176895, A180001, A334496, A334499-A334515.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, May 05 2020
%E More terms from _Jinyuan Wang_, May 09 2020
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