(Translated by https://www.hiragana.jp/)
A267044 - OEIS
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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.
2
1, 10, 100, 1000, 10001, 100010, 1000101, 10001010, 100010101, 1000101010, 10001010101, 100010101010, 1000101010101, 10001010101010, 100010101010101, 1000101010101010, 10001010101010101, 100010101010101010, 1000101010101010101, 10001010101010101010
OFFSET
0,2
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
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>4. [Typo corrected by Karl V. Keller, Jr., Mar 16 2022]
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
Sequence in context: A290299 A138824 A273495 * A266445 A266896 A282981
KEYWORD
nonn
AUTHOR
Robert Price, Jan 09 2016
EXTENSIONS
Removed an unjustified claim that Colin Barker's conjectures are correct. Removed a program based on a conjecture. - Michael De Vlieger, Jun 13 2022
STATUS
approved