A266680 Binary representation of the middle column of the "Rule 175" elementary cellular automaton starting with a single ON (black) cell.

1, 11, 110, 1101, 11011, 110111, 1101111, 11011111, 110111111, 1101111111, 11011111111, 110111111111, 1101111111111, 11011111111111, 110111111111111, 1101111111111111, 11011111111111111, 110111111111111111, 1101111111111111111, 11011111111111111111

Offset: 0

Author

Robert Price, Jan 18 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. A265186, A266678, A267604.

Programs

Mathematica

rule=175; 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 *) mc=Table[catri[[k]][[k]],{k,1,rows}]; (* keep only middle cell from each row *) Table[FromDigits[Take[mc,k]],{k,1,rows}]  (* binary representation of middle column *)

Formula

Conjectures from Colin Barker, Jan 19 2016 and Apr 18 2019: (Start)

a(n) = 11*a(n-1) - 10*a(n-2) for n > 3.

G.f.: (1-x^2+x^3) / ((1-x)*(1-10*x)).

(End)