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A266435
Binary representation of the n-th iteration of the "Rule 23" elementary cellular automaton starting with a single ON (black) cell.
3
1, 111, 0, 1111111, 0, 11111111111, 0, 111111111111111, 0, 1111111111111111111, 0, 11111111111111111111111, 0, 111111111111111111111111111, 0, 1111111111111111111111111111111, 0, 11111111111111111111111111111111111, 0, 111111111111111111111111111111111111111
OFFSET
0,2
COMMENTS
Rules 31, 55, 63, 87, 95, 119 and 127 also generate this sequence.
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
FORMULA
From Colin Barker, Dec 30 2015 and Apr 15 2019: (Start)
a(n) = ((-1)^n-1)*(1-10^(2*n+1))/18 for n>0.
a(n) = 10001*a(n-2)-10000*a(n-4) for n>4.
G.f.: (1+111*x-10001*x^2+1000*x^3+10000*x^4) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)).
(End)
a(n) = (10*100^n-1)/9*(n mod 2) + 0^n. - Karl V. Keller, Jr., Aug 11 2021
MATHEMATICA
rule=23; 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 *) Table[FromDigits[catri[[k]]], {k, 1, rows}] (* Binary Representation of Rows *)
PROG
(Python) print([(10*100**n-1)//9*(n%2) + 0**n for n in range(33)]) # Karl V. Keller, Jr., Aug 11 2021
CROSSREFS
Sequence in context: A280141 A280142 A077573 * A216479 A123698 A123727
KEYWORD
nonn,easy
AUTHOR
Robert Price, Dec 29 2015
STATUS
approved