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A265381 Decimal representation of the middle column of the "Rule 158" elementary cellular automaton starting with a single ON (black) cell. 3

%I

%S 1,3,7,14,29,59,119,238,477,955,1911,3822,7645,15291,30583,61166,

%T 122333,244667,489335,978670,1957341,3914683,7829367,15658734,

%U 31317469,62634939,125269879,250539758,501079517,1002159035,2004318071,4008636142,8017272285

%N Decimal representation of the middle column of the "Rule 158" elementary cellular automaton starting with a single ON (black) cell.

%D S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

%H Robert Price, <a href="/A265381/b265381.txt">Table of n, a(n) for n = 0..999</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>

%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>

%H <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>

%F Conjectures from _Colin Barker_, Dec 07 2015 and Apr 16 2019: (Start)

%F a(n) = (-45+5*(-1)^n-(6-i*3)*(-i)^n-(6+3*i)*i^n+7*2^(4+n))/60 where i = sqrt(-1).

%F a(n) = 2*a(n-1)+a(n-4)-2*a(n-5) for n>4.

%F G.f.: (1+x+x^2) / ((1-x)*(1+x)*(1-2*x)*(1+x^2)).

%F (End)

%e From _Michael De Vlieger_, Dec 09 2015: (Start)

%e First 8 rows at left, ignoring "0" outside of range of 1's, the center column values in parentheses. The center column values up to that row are concatenated then converted into decimal at right:

%e Rule 158 Binary Decimal

%e (1) -> 1 = 1

%e 1 (1) 1 -> 11 = 3

%e 1 1 (1) 0 1 -> 111 = 7

%e 1 1 1 (0) 0 1 1 -> 1110 = 14

%e 1 1 1 0 (1) 1 1 0 1 -> 11101 = 29

%e 1 1 1 0 0 (1) 1 0 0 1 1 -> 111011 = 59

%e 1 1 1 0 1 1 (1) 0 1 1 1 0 1 -> 1110111 = 119

%e 1 1 1 0 0 1 1 (0) 0 1 1 0 0 1 1 -> 11101110 = 238

%e 1 1 1 0 1 1 1 0 (1) 1 1 0 1 1 1 0 1 -> 111011101 = 477

%e (End)

%t f[n_] := Block[{w = {}}, Do[AppendTo[w, Boole[Mod[k, 4] != 3]], {k, 0, n}]; FromDigits[w, 2]]; Table[f@ n, {n, 0, 32}] (* _Michael De Vlieger_, Dec 09 2015 *)

%Y Cf. A071037.

%K nonn,easy

%O 0,2

%A _Robert Price_, Dec 07 2015

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Last modified August 13 04:54 EDT 2020. Contains 336442 sequences. (Running on oeis4.)