A267880 Decimal representation of the middle column of the "Rule 233" elementary cellular automaton starting with a single ON (black) cell.

1, 2, 5, 10, 21, 43, 87, 175, 351, 703, 1407, 2815, 5631, 11263, 22527, 45055, 90111, 180223, 360447, 720895, 1441791, 2883583, 5767167, 11534335, 23068671, 46137343, 92274687, 184549375, 369098751, 738197503, 1476395007, 2952790015, 5905580031, 11811160063

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 22 2016 and Apr 20 2019: (Start)

a(n) = 3*a(n-1)-2*a(n-2) for n>4.

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

(End)

Mathematica

rule=233; 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. A267868.

Sequence in context: A266248 A027437 A267444 * A101510 A066819 A114279

Adjacent sequences: A267877 A267878 A267879 * A267881 A267882 A267883

Keyword

nonn,easy

Author

Robert Price, Jan 21 2016

Status

approved