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A267127
Binary representation of the n-th iteration of the "Rule 99" elementary cellular automaton starting with a single ON (black) cell.
1
1, 100, 1010, 1101001, 1100100, 11101010011, 1101001000, 111101100100111, 1101010010000, 1111101101001001111, 1101100100100000, 11111101101010010011111, 1101101001001000000, 111111101101100100100111111, 1101101010010010000000, 1111111101101101001001001111111
OFFSET
0,2
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
FORMULA
Empirical g.f.: (1 +100*x -10001*x^2 -1099*x^3 -10000*x^5 -899991000*x^6 +10000000*x^7 +10911000000*x^8 -20000000000*x^10) / ((1 -x)*(1 +x)*(1 -10*x)*(1 -100*x)*(1 +100*x)*(1 -10*x^2)*(1 +10*x +100*x^2)*(1 -1000*x^2)). - Colin Barker, Jan 11 2016 and Apr 19 2019
MATHEMATICA
rule=99; 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 *)
CROSSREFS
Cf. A267126.
Sequence in context: A136387 A001737 A266838 * A266893 A267153 A343294
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 10 2016
STATUS
approved