A267366 Binary representation of the middle column of the "Rule 126" elementary cellular automaton starting with a single ON (black) cell.

1, 11, 110, 1101, 11010, 110100, 1101000, 11010001, 110100010, 1101000100, 11010001000, 110100010000, 1101000100000, 11010001000000, 110100010000000, 1101000100000001, 11010001000000010, 110100010000000100, 1101000100000001000, 11010001000000010000

Offset: 0

Author

Robert Price, Jan 13 2016

Keywords

• nonn
• easy

Comments

The middle column itself is A036987. [Noticed by Dominik Koeppl, Oct 21 2022]

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. A267367 (decimal), A071035, A036987, A209229.

Programs

Mathematica

rule=126; 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 *)