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A267604 Decimal representation of the middle column of the "Rule 175" elementary cellular automaton starting with a single ON (black) cell. 3
1, 3, 6, 13, 27, 55, 111, 223, 447, 895, 1791, 3583, 7167, 14335, 28671, 57343, 114687, 229375, 458751, 917503, 1835007, 3670015, 7340031, 14680063, 29360127, 58720255, 117440511, 234881023, 469762047, 939524095, 1879048191, 3758096383, 7516192767 (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
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
FORMULA
Conjectures from Colin Barker, Jan 18 2016 and Apr 20 2019: (Start)
a(n) = 3*a(n-1)-2*a(n-2) for n>3.
G.f.: (1-x^2+x^3) / ((1-x)*(1-2*x)). (End)
Conjectures from Altug Alkan, Jan 18 2016: (Start)
a(n) = A086224(n-2), for n > 1.
a(n) = ceiling((7/4)*2^n - 1). (End)
MATHEMATICA
rule=175; 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
Sequence in context: A055143 A092539 A094386 * A099036 A131246 A183314
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 18 2016
STATUS
approved

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Last modified May 29 12:05 EDT 2024. Contains 372940 sequences. (Running on oeis4.)