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A118171 Decimal representation of n-th iteration of the Rule 158 elementary cellular automaton starting with a single black cell. 2
1, 7, 29, 115, 477, 1843, 7645, 29491, 122333, 471859, 1957341, 7549747, 31317469, 120795955, 501079517, 1932735283, 8017272285, 30923764531, 128276356573, 494780232499, 2052421705181, 7916483719987, 32838747282909, 126663739519795, 525419956526557 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Rule 158

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

Index entries for linear recurrences with constant coefficients, signature (0,17,0,-16).

Index entries for sequences related to cellular automata

FORMULA

a(n) = (1/30)*(-16+(-4)^n-10*(-1)^n+55*4^n).

From Colin Barker, Oct 08 2015: (Start)

a(n) = 17*a(n-2) - 16*a(n-4) for n>3.

G.f.: -(4*x^3-12*x^2-7*x-1) / ((x-1)*(x+1)*(4*x-1)*(4*x+1)).

(End)

EXAMPLE

            1;

         1, 1, 1;

      1, 1, 1, 0, 1;

   1, 1, 1, 0, 0, 1, 1;

1, 1, 1, 0, 1, 1, 1, 0, 1;

...

From Michael De Vlieger, Oct 08 2015: (Start)

First 8 rows, representing ON cells as "1", OFF cells within the bounds

of ON cells as "0", interpreted as a binary number at left, the decimal

equivalent appearing at right:

                   1 =      1

                 111 =      7

              1 1101 =     29

            111 0011 =    115

         1 1101 1101 =    477

       111 0011 0011 =   1843

    1 1101 1101 1101 =   7645

  111 0011 0011 0011 =  29491

11101 1101 1101 1101 = 122333

(End)

MATHEMATICA

Table[(-16 + (-4)^n - 10 (-1)^n + 55*4^n)/30, {n, 0, 24}] (* or *)

clip[lst_] := Block[{p = Flatten@ Position[lst, 1]}, Take[lst, {Min@ p, Max@ p}]]; FromDigits[#, 2] & /@ Map[clip, CellularAutomaton[158, {{1}, 0}, 24]] (* Michael De Vlieger, Oct 08 2015 *)

PROG

(PARI) Vec(-(4*x^3-12*x^2-7*x-1)/((x-1)*(x+1)*(4*x-1)*(4*x+1)) + O(x^30)) \\ Colin Barker, Oct 08 2015

(PARI) vector(100, n, n--; (1/30)*(-16+(-4)^n-10*(-1)^n+55*4^n)) \\ Altug Alkan, Oct 08 2015

CROSSREFS

Cf. A071037.

Sequence in context: A049349 A124828 A037094 * A072261 A066744 A037576

Adjacent sequences:  A118168 A118169 A118170 * A118172 A118173 A118174

KEYWORD

nonn,base,easy

AUTHOR

Eric W. Weisstein, Apr 13 2006

STATUS

approved

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Last modified May 1 13:35 EDT 2016. Contains 272254 sequences.