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1, 111, 11111, 1111111, 111111111, 11111111111, 1111111111111, 111111111111111, 11111111111111111, 1111111111111111111, 111111111111111111111, 11111111111111111111111
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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COMMENTS
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Also the binary representation of the n-th iteration of the elementary cellular automaton starting with a single ON (black) cell for Rules 151, 159, 183, 191, 215, 222, 223, 247, 254 and 255. - Robert Price, Feb 21 2016
The aerated sequence 1, 0, 111, 0, 11111, 0, 1111111, ... is a linear divisibility sequence of order 4. It is the case P1 = 0, P2 = -9^2, Q = -10 of the 3-parameter family of 4th-order linear divisibility sequences found by Williams and Guy. Cf. A007583, A095372 and A299960. - Peter Bala, Aug 28 2019
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REFERENCES
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S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
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LINKS
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Table of n, a(n) for n=0..11.
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
H. C. Williams and R. K. Guy, Some fourth-order linear divisibility sequences, Intl. J. Number Theory 7 (5) (2011) 1255-1277.
H. C. Williams and R. K. Guy, Some Monoapparitic Fourth Order Linear Divisibility Sequences Integers, Volume 12A (2012) The John Selfridge Memorial Volume.
S. Wolfram, A New Kind of Science
Index to Elementary Cellular Automata
Index entries for sequences related to cellular automata
Index entries for linear recurrences with constant coefficients, signature (101,-100).
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FORMULA
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Numbers composed entirely of 2*n+1 concatenated 1's for n >= 0.
O.g.f.: (1+10*x)/((-1+x)*(-1+100*x)). - R. J. Mathar, Apr 03 2008
From Klaus Purath, Sep 23 2020: (Start)
a(n) = Sum_{i = 0..2*n} 10^i.
a(n) = 101*a(n-1) - 100*a(n-2).
a(n) = 110*10^(2*n-2) + a(n-1).
a(n) = 100*a(n-1) + 11.
a(n) = (a(n-1)^2 - 1210*10^(2*n-4))/a(n-2). (End)
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MAPLE
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seq((10^(2*n+1) - 1)/9, n=0..15); # C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 19 2005
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MATHEMATICA
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Table[(10^(2*n + 1) - 1)/9, {n, 0, 100}] (* Robert Price, Feb 21 2016 *)
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CROSSREFS
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Cf. A002275, A099814 (other bisection), A007583, A095372, A299960.
Sequence in context: A265379 A265688 A138146 * A259102 A262629 A111864
Adjacent sequences: A100703 A100704 A100705 * A100707 A100708 A100709
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Nov 19 2004
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EXTENSIONS
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More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 19 2005
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STATUS
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approved
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