A267514 Binary representation of the middle column of the "Rule 137" elementary cellular automaton starting with a single ON (black) cell.

1, 10, 101, 1010, 10101, 101010, 1010100, 10101001, 101010010, 1010100101, 10101001010, 101010010101, 1010100101010, 10101001010100, 101010010101001, 1010100101010010, 10101001010100101, 101010010101001010, 1010100101010010101, 10101001010100101010

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

a(n) = A007088(A267515(n)). - R. J. Mathar, Apr 12 2019

Conjectures from Colin Barker, Jan 16 2016: (Start)

a(n) = 10*a(n-1)+a(n-7)-10*a(n-8) for n>7.

G.f.: (1-x+x^2)*(1+x+x^2) / ((1-x)*(1-10*x)*(1+x+x^2+x^3+x^4+x^5+x^6)).

(End)

This conjectured linear recurrence fails to predict the correct values from a(62) on. - R. J. Mathar, Apr 12 2019

Mathematica

rule=137; 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. A267463.

Sequence in context: A303596 A266612 A267588 * A279809 A279749 A056830

Adjacent sequences: A267511 A267512 A267513 * A267515 A267516 A267517

Keyword

nonn,easy

Author

Robert Price, Jan 16 2016

Status

approved