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A267044 Binary representation of the middle column of the "Rule 91" elementary cellular automaton starting with a single ON (black) cell. 1
1, 10, 100, 1000, 10001, 100010, 1000101, 10001010, 100010101, 1000101010, 10001010101, 100010101010, 1000101010101, 10001010101010, 100010101010101, 1000101010101010, 10001010101010101, 100010101010101010, 1000101010101010101, 10001010101010101010 (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

FORMULA

Conjectures from Colin Barker, Jan 10 2016: (Start)

a(n) = (-550+450*(-1)^n+9901*10^n)/9900 for n>1.

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

G.f.: (1-x^2+x^4) / ((1-x)*(1+x)*(1-10*x)).

(End)

MATHEMATICA

rule=91; 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 *)

CROSSREFS

Cf. A267015.

Sequence in context: A290299 A138824 A273495 * A266445 A266896 A282981

Adjacent sequences:  A267041 A267042 A267043 * A267045 A267046 A267047

KEYWORD

nonn

AUTHOR

Robert Price, Jan 09 2016

STATUS

approved

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Last modified September 18 10:31 EDT 2020. Contains 337166 sequences. (Running on oeis4.)