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A267210 Decimal representation of the middle column of the "Rule 109" elementary cellular automaton starting with a single ON (black) cell. 1
1, 3, 7, 14, 29, 59, 118, 237, 475, 950, 1901, 3803, 7606, 15213, 30427, 60854, 121709, 243419, 486838, 973677, 1947355, 3894710, 7789421, 15578843, 31157686, 62315373, 124630747, 249261494, 498522989, 997045979, 1994091958, 3988183917, 7976367835 (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 13 2016 and Apr 19 2019: (Start)

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

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

(End)

MATHEMATICA

rule=109; 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. A243566.

Sequence in context: A125899 A266791 A052997 * A074988 A265381 A066225

Adjacent sequences:  A267207 A267208 A267209 * A267211 A267212 A267213

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 11 2016

STATUS

approved

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Last modified July 5 03:05 EDT 2020. Contains 335457 sequences. (Running on oeis4.)