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A266592 Binary representation of the middle column of the "Rule 37" elementary cellular automaton starting with a single ON (black) cell. 1
1, 11, 111, 1110, 11101, 111010, 1110101, 11101010, 111010101, 1110101010, 11101010101, 111010101010, 1110101010101, 11101010101010, 111010101010101, 1110101010101010, 11101010101010101, 111010101010101010, 1110101010101010101, 11101010101010101010 (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..1000

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

S. Wolfram, A New Kind of Science

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Index entries for linear recurrences with constant coefficients, signature (10,1,-10).

FORMULA

From Colin Barker, Jan 02 2016: (Start)

a(n) = (45*(-1)^n+1099*10^n-55)/990 for n>0.

a(n) = 10*a(n-1)+a(n-2)-10*a(n-3) for n>3.

G.f.: (1+x-x^3) / ((1-x)*(1+x)*(1-10*x)).

(End)

MATHEMATICA

rule=37; rows=20; ca=CellularAutomaton[rule, {{1}, 0}, rows-1, {All, All}]; (* Start with single black cell *) catri=Table[Take[ca[[k]], {rows-k+1, rows+k-1}], {k, 1, rows}]; (* Truncated list of each row *) mc=Table[catri[[k]][[k]], {k, 1, rows}]; (* Keep only middle cell from each row *) Table[FromDigits[Take[mc, k]], {k, 1, rows}]  (* Binary Representation of Middle Column *)

Join[{1}, LinearRecurrence[{10, 1, -10}, {11, 111, 1110}, 26]] (* Vincenzo Librandi, Jan 02 2016 *)

PROG

(PARI) Vec((1+x-x^3)/((1-x)*(1+x)*(1-10*x)) + O(x^30)) \\ Colin Barker, Jan 02 2016

(MAGMA) I:=[1, 11, 111, 1110]; [n le 4 select I[n] else 10*Self(n-1)+Self(n-2)-10*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jan 02 2016

CROSSREFS

Cf. A266588.

Sequence in context: A110437 A266624 A266790 * A267209 A110444 A265380

Adjacent sequences:  A266589 A266590 A266591 * A266593 A266594 A266595

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 01 2016

STATUS

approved

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Last modified March 26 04:32 EDT 2019. Contains 321481 sequences. (Running on oeis4.)