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A266680 Binary representation of the middle column of the "Rule 175" elementary cellular automaton starting with a single ON (black) cell. 1
1, 11, 110, 1101, 11011, 110111, 1101111, 11011111, 110111111, 1101111111, 11011111111, 110111111111, 1101111111111, 11011111111111, 110111111111111, 1101111111111111, 11011111111111111, 110111111111111111, 1101111111111111111, 11011111111111111111 (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 (11,-10).

FORMULA

From Colin Barker, Jan 19 2016: (Start)

a(n) = 11*a(n-1)-10*a(n-2) for n>3.

G.f.: (1-x^2+x^3) / ((1-x)*(1-10*x)).

(End)

MATHEMATICA

rule=175; 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 *)

PROG

(PARI) Vec((1-x^2+x^3)/((1-x)*(1-10*x)) + O(x^20)) \\ Colin Barker, Jan 19 2016

CROSSREFS

Cf. A265186.

Sequence in context: A065829 A261299 A081933 * A036843 A299301 A278786

Adjacent sequences:  A266677 A266678 A266679 * A266681 A266682 A266683

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 18 2016

STATUS

approved

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Last modified October 22 23:18 EDT 2018. Contains 316518 sequences. (Running on oeis4.)