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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. 1
 1, 11, 111, 1110, 11101, 111011, 1110111, 11101110, 111011101, 1110111011, 11101110111, 111011101110, 1110111011101, 11101110111011, 111011101110111, 1110111011101110, 11101110111011101, 111011101110111011, 1110111011101110111, 11101110111011101110 (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..999 Eric Weisstein's World of Mathematics, Elementary Cellular Automaton 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 *) LinearRecurrence[{10, 0, 0, 1, -10}, {1, 11, 111, 1110, 11101}, 20] (* Harvey P. Dale, May 17 2017 *) CROSSREFS Cf. A071037, A265381. Sequence in context: A266592 A267209 A110444 * A114397 A336325 A098595 Adjacent sequences:  A265377 A265378 A265379 * A265381 A265382 A265383 KEYWORD nonn,easy AUTHOR Robert Price, Dec 07 2015 STATUS approved

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Last modified August 11 06:10 EDT 2020. Contains 336422 sequences. (Running on oeis4.)