A266592 Binary representation of the middle column of the "Rule 37" elementary cellular automaton starting with a single ON (black) cell.

1, 11, 111, 1110, 11101, 111010, 1110101, 11101010, 111010101, 1110101010, 11101010101, 111010101010, 1110101010101, 11101010101010, 111010101010101, 1110101010101010, 11101010101010101, 111010101010101010, 1110101010101010101, 11101010101010101010

Offset

0,2

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

Formula

Conjectures from Colin Barker, Jan 02 2016 and Apr 18 2019: (Start)

a(n) = (45*(-1)^n+1099*10^n-55)/990 for n>0.

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

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

(End)

Mathematica

rule=37; 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. A266588.

Sequence in context: A110437 A266624 A266790 * A267209 A110444 A265380

Adjacent sequences: A266589 A266590 A266591 * A266593 A266594 A266595

Keyword

nonn,easy

Author

Robert Price, Jan 01 2016

Status

approved