A267051 Binary representation of the n-th iteration of the "Rule 92" elementary cellular automaton starting with a single ON (black) cell.

1, 11, 111, 1011, 10111, 101011, 1010111, 10101011, 101010111, 1010101011, 10101010111, 101010101011, 1010101010111, 10101010101011, 101010101010111, 1010101010101011, 10101010101010111, 101010101010101011, 1010101010101010111, 10101010101010101011

Offset: 0

Author

Robert Price, Jan 09 2016

Keywords

• nonn
• easy

References

• S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

Links

• Robert Price, Table of n, a(n) for n = 0..1000
• Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
• S. Wolfram, A New Kind of Science
• Index entries for sequences related to cellular automata
• Index to Elementary Cellular Automata

Crossrefs

Cf. A267050, A267052.

Programs

Mathematica

rule=92; 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 10 2016 and Apr 17 2019: (Start)

a(n) = (539+450*(-1)^n+10^(2+n))/99 for n>0.

a(n) = 10*a(n-1)+a(n-2)-10*a(n-3) for n>3.

G.f.: (1+x-100*x^3) / ((1-x)*(1+x)*(1-10*x)).

(End)