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A267880 Decimal representation of the middle column of the "Rule 233" elementary cellular automaton starting with a single ON (black) cell. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 25 12:30 EDT 2019. Contains 323568 sequences. (Running on oeis4.)