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A266299
Binary representation of the n-th iteration of the "Rule 14" elementary cellular automaton starting with a single ON (black) cell.
5
1, 110, 11000, 1100000, 110000000, 11000000000, 1100000000000, 110000000000000, 11000000000000000, 1100000000000000000, 110000000000000000000, 11000000000000000000000, 1100000000000000000000000, 110000000000000000000000000, 11000000000000000000000000000
OFFSET
0,2
COMMENTS
Rules 46, 142 and 174 also generate this sequence.
FORMULA
From Colin Barker, Dec 28 2015 and Apr 14 2019: (Start)
a(n) = 11*10^(2*n-1) for n>0.
a(n) = 100*a(n-1) for n>1.
G.f.: (1+10*x) / (1-100*x).
(End)
a(n) = floor(110*100^(n-1)). - Karl V. Keller, Jr., Aug 30 2021
MATHEMATICA
rule=14; 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 *)
LinearRecurrence[{100}, {1, 110}, 20] (* Harvey P. Dale, Aug 27 2023 *)
PROG
(Python) print([int(110*100**(n-1)) for n in range(50)]) # Karl V. Keller, Jr., Aug 30 2021
CROSSREFS
Sequence in context: A265319 A267854 A135645 * A265696 A267535 A267577
KEYWORD
nonn,easy
AUTHOR
Robert Price, Dec 26 2015
STATUS
approved