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A265380
Binary representation of the middle column of the "Rule 158" elementary cellular automaton starting with a single ON (black) cell.
3
1, 11, 111, 1110, 11101, 111011, 1110111, 11101110, 111011101, 1110111011, 11101110111, 111011101110, 1110111011101, 11101110111011, 111011101110111, 1110111011101110, 11101110111011101, 111011101110111011, 1110111011101110111, 11101110111011101110
OFFSET
0,2
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
FORMULA
Conjectures from Colin Barker, Dec 14 2015 and Apr 18 2019: (Start)
a(n) = 10*a(n-1) + a(n-4) - 10*a(n-5) for n>4.
G.f.: (1+x+x^2) / ((1-x)*(1+x)*(1-10*x)*(1+x^2)).
(End)
EXAMPLE
From Michael De Vlieger, Dec 09 2015: (Start)
First 8 rows at left, ignoring "0" outside of range of 1's, the center column values in parentheses, and at right the value of center column cells up to that row :
(1) -> 1
1 (1) 1 -> 11
1 1 (1) 0 1 -> 111
1 1 1 (0) 0 1 1 -> 1110
1 1 1 0 (1) 1 1 0 1 -> 11101
1 1 1 0 0 (1) 1 0 0 1 1 -> 111011
1 1 1 0 1 1 (1) 0 1 1 1 0 1 -> 1110111
1 1 1 0 0 1 1 (0) 0 1 1 0 0 1 1 -> 11101110
1 1 1 0 1 1 1 0 (1) 1 1 0 1 1 1 0 1 -> 111011101
1 1 1 0 0 1 1 0 0 (1) 1 0 0 1 1 0 0 1 1 -> 1110111011
1 1 1 0 1 1 1 0 1 1 (1) 0 1 1 1 0 1 1 1 0 1 -> 11101110111
1 1 1 0 0 1 1 0 0 1 1 (0) 0 1 1 0 0 1 1 0 0 1 1 -> 111011101110
1 1 1 0 1 1 1 0 1 1 1 0 (1) 1 1 0 1 1 1 0 1 1 1 0 1 -> 1110111011101
(End)
MATHEMATICA
f[n_] := Block[{w = {}}, Do[AppendTo[w, Boole[Mod[k, 4] != 3]], {k, 0, n}]; FromDigits@ w]; Table[f@ n, {n, 0, 19}] (* Michael De Vlieger, Dec 09 2015 *)
CROSSREFS
Sequence in context: A266592 A267209 A110444 * A114397 A336325 A098595
KEYWORD
nonn,easy
AUTHOR
Robert Price, Dec 07 2015
EXTENSIONS
Removed an unjustified claim that Colin Barker's conjectures are correct. Removed 2 programs based on conjectures. - N. J. A. Sloane, Jun 13 2022
STATUS
approved