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A266508 Binary representation of the n-th iteration of the "Rule 28" elementary cellular automaton starting with a single ON (black) cell. 6
1, 11, 101, 1011, 10101, 101011, 1010101, 10101011, 101010101, 1010101011, 10101010101, 101010101011, 1010101010101, 10101010101011, 101010101010101, 1010101010101011, 10101010101010101, 101010101010101011, 1010101010101010101, 10101010101010101011 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Rule 156 also generates this sequence.
Also, the binary representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 678", based on the 5-celled von Neumann neighborhood, initialized with a single black (ON) cell at stage zero. See A283641.
LINKS
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
FORMULA
From Colin Barker, Dec 30 2015 and Apr 16 2019: (Start)
a(n) = (44 - 45*(-1)^n + 10^(2+n))/99.
a(n) = 10*a(n-1) + a(n-2) - 10*a(n-3) for n>2.
G.f.: (1+x-10*x^2) / ((1-x)*(1+x)*(1-10*x)).
(End)
a(n) = floor((100*10^n + 89)/99). - Karl V. Keller, Jr., Sep 04 2021
MATHEMATICA
rule=28; 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]]], {k, 1, rows}] (* Binary Representation of Rows *)
PROG
(Python) print([(100*10**n + 89)//99 for n in range(50)]) # Karl V. Keller, Jr., Sep 04 2021
CROSSREFS
Sequence in context: A283582 A283700 A284537 * A284424 A284545 A283645
KEYWORD
nonn,easy
AUTHOR
Robert Price, Dec 30 2015
STATUS
approved

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Last modified March 28 15:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)