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

1, 3, 7, 14, 29, 59, 119, 238, 477, 955, 1911, 3822, 7645, 15291, 30583, 61166, 122333, 244667, 489335, 978670, 1957341, 3914683, 7829367, 15658734, 31317469, 62634939, 125269879, 250539758, 501079517, 1002159035, 2004318071, 4008636142, 8017272285

Offset

0,2

Links

Robert Price, Table of n, a(n) for n = 0..999

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

Eric Weisstein's World of Mathematics, Rule 158

Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Index entries for linear recurrences with constant coefficients, signature (2,0,0,1,-2).

Formula

From Colin Barker, Dec 07 2015 and Apr 16 2019: (Start)

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).

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

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

(End)

a(n) = floor(7*2^(n+2)/15) for n>=0. - Karl V. Keller, Jr., Oct 01 2020

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. The center column values up to that row are concatenated then converted into decimal at right:
             Rule 158                   Binary     Decimal
                (1)                 ->         1 =   1
              1 (1) 1               ->        11 =   3
            1 1 (1) 0 1             ->       111 =   7
          1 1 1 (0) 0 1 1           ->      1110 =  14
        1 1 1 0 (1) 1 1 0 1         ->     11101 =  29
      1 1 1 0 0 (1) 1 0 0 1 1       ->    111011 =  59
    1 1 1 0 1 1 (1) 0 1 1 1 0 1     ->   1110111 = 119
  1 1 1 0 0 1 1 (0) 0 1 1 0 0 1 1   ->  11101110 = 238
1 1 1 0 1 1 1 0 (1) 1 1 0 1 1 1 0 1 -> 111011101 = 477
(End)

Mathematica

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 *)

Prog

(Python) print([7*2**(n+2)//15 for n in range(34)]) # Karl V. Keller, Jr., Oct 01 2020

Crossrefs

Cf. A071037, A265380 (binary).

Sequence in context: A052997 A267210 A074988 * A066225 A305777 A139817

Adjacent sequences: A265378 A265379 A265380 * A265382 A265383 A265384

Keyword

nonn,easy

Author

Robert Price, Dec 07 2015

Status

approved