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A265688
Binary representation of the n-th iteration of the "Rule 190" elementary cellular automaton starting with a single ON (black) cell.
3
1, 111, 11101, 1110111, 111011101, 11101110111, 1110111011101, 111011101110111, 11101110111011101, 1110111011101110111, 111011101110111011101, 11101110111011101110111, 1110111011101110111011101, 111011101110111011101110111, 11101110111011101110111011101
OFFSET
0,2
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
FORMULA
From Colin Barker, Dec 13 2015 and Apr 18 2019: (Start)
a(n) = (-165*(-1)^n+37*100^(n+1)-202)/3333.
a(n) = (37*100^(n+1)-367)/3333 for n even.
a(n) = (37*100^(n+1)-37)/3333 for n odd.
a(n) = 100*a(n-1) + a(n-2) - 100*a(n-3) for n>2.
G.f.: (1+11*x) / ((1-x)*(1+x)*(1-100*x)).
(End)
a(n) = floor(11100*100^n/9999). - Karl V. Keller, Jr., Aug 10 2021
MATHEMATICA
rule = 190; rows = 20; Table[FromDigits[Table[Take[CellularAutomaton[rule, {{1}, 0}, rows-1, {All, All}][[k]], {rows-k+1, rows+k-1}], {k, 1, rows}][[k]]], {k, 1, rows}]
PROG
(Python) print([11100*100**n//9999 for n in range(30)]) # Karl V. Keller, Jr., Aug 10 2021
CROSSREFS
Cf. A037576 (decimal), A118111.
Sequence in context: A071033 A267364 A265379 * A138146 A100706 A259102
KEYWORD
nonn,easy
AUTHOR
Robert Price, Dec 13 2015
STATUS
approved