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URL: https://oeis.org/A267774

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A267774
Decimal representation of the n-th iteration of the "Rule 207" elementary cellular automaton starting with a single ON (black) cell.
2
1, 6, 29, 123, 503, 2031, 8159, 32703, 130943, 524031, 2096639, 8387583, 33552383, 134213631, 536862719, 2147467263, 8589901823, 34359672831, 137438822399, 549755551743, 2199022731263, 8796091973631, 35184369991679, 140737484161023, 562949945032703
OFFSET
0,2
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
FORMULA
Conjectures from Colin Barker, Jan 20 2016 and Apr 20 2019: (Start)
a(n) = 7*a(n-1)-14*a(n-2)+8*a(n-3) for n>3.
G.f.: (1-x+x^2-4*x^3) / ((1-x)*(1-2*x)*(1-4*x)).
(End)
MATHEMATICA
rule=207; 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 *) Table[FromDigits[catri[[k]], 2], {k, 1, rows}] (* Decimal Representation of Rows *)
CROSSREFS
Sequence in context: A326805 A061648 A281050 * A243474 A111644 A225618
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 20 2016
EXTENSIONS
Removed an unjustified claim that Colin Barker's conjectures are correct. Removed a program based on a conjecture. - Michael De Vlieger, Jun 13 2022
STATUS
approved