A266790 Binary representation of the middle column of the "Rule 61" elementary cellular automaton starting with a single ON (black) cell.

1, 11, 111, 1110, 11101, 111010, 1110101, 11101010, 111010100, 1110101001, 11101010011, 111010100111, 1110101001110, 11101010011101, 111010100111010, 1110101001110101, 11101010011101010, 111010100111010101, 1110101001110101010, 11101010011101010101

Offset

0,2

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

Formula

Conjectures from Colin Barker, Jan 04 2016 and Apr 18 2019: (Start)

a(n) = (-9*(-1)^n+1098999991099*2^(n-9)*5^(n-10)-11)/198 for n>9.

G.f.: (1+x-x^3-x^8+x^9+x^10-x^12) / ((1-x)*(1+x)*(1-10*x)).

(End)

Mathematica

rule=61; 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 *)

Crossrefs

Cf. A266786, A266789, A266791.

Sequence in context: A284540 A110437 A266624 * A266592 A267209 A110444

Adjacent sequences: A266787 A266788 A266789 * A266791 A266792 A266793

Keyword

nonn,easy

Author

Robert Price, Jan 03 2016

Status

approved