A267258 Decimal representation of the middle column of the "Rule 111" elementary cellular automaton starting with a single ON (black) cell.

1, 3, 7, 15, 31, 63, 127, 255, 510, 1021, 2042, 4085, 8170, 16341, 32682, 65365, 130730, 261461, 522922, 1045845, 2091690, 4183381, 8366762, 16733525, 33467050, 66934101, 133868202, 267736405, 535472810, 1070945621, 2141891242, 4283782485, 8567564970

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 13 2016 and Apr 17 2019: (Start)

a(n) = (383*2^n-32*((-1)^n+3))/192 for n>5.

G.f.: (1+x-x^8) / ((1-x)*(1+x)*(1-2*x)).

(End)

Mathematica

rule=111; 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], 2], {k, 1, rows}]  (* Binary Representation of Middle Column *)

Crossrefs

Cf. A267253.

Sequence in context: A043747 A105754 A116690 * A305493 A213247 A043755

Adjacent sequences: A267255 A267256 A267257 * A267259 A267260 A267261

Keyword

nonn,easy

Author

Robert Price, Jan 12 2016

Status

approved