A266660 Binary representation of the n-th iteration of the "Rule 47" elementary cellular automaton starting with a single ON (black) cell.
1, 110, 11, 1111100, 11, 11111111100, 11, 111111111111100, 11, 1111111111111111100, 11, 11111111111111111111100, 11, 111111111111111111111111100, 11, 1111111111111111111111111111100, 11, 11111111111111111111111111111111100, 11
Offset: 0
Links
- Robert Price, Table of n, a(n) for n = 0..1000
- Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
- Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
- Index entries for sequences related to cellular automata
- Index to Elementary Cellular Automata
Programs
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Mathematica
rule=47; rows=20; ca=CellularAutomaton[rule,{{1},0},rows-1,{All,All}]; (* Start with single black cell *) catri=Table[Take[ca[[k]],{rows-k+1,rows+k-1}],{k,1,rows}]; (* Truncated list of each row *) Table[FromDigits[catri[[k]]],{k,1,rows}] (* Binary Representation of Rows *)
Formula
Conjectures from Colin Barker, Jan 03 2016 and Apr 18 2019: (Start)
a(n) = (199*(-1)^n+10^(2*n+1)-(-1)^n*10^(2*n+1)-1)/18 for n>1.
a(n) = 10001*a(n-2)-10000*a(n-4) for n>5.
G.f.: (1+110*x-9990*x^2+10990*x^3-100000*x^4+100000*x^5) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)).
(End)
a(n) = A266254(n), n>1. - R. J. Mathar, Jan 10 2016
Conjecture: a(n) = (10*100^n - 100)/9 for odd n > 1; a(n) = 11 for even n > 1. - Karl V. Keller, Jr., Oct 10 2021