OFFSET
0,2
COMMENTS
More precisely, this is the orbit of the initial value 1 under this Rule 230, cf. A292682. The substitution 100 -> 0 ensures that the initial 1 never extends to the right. - M. F. Hasler, Oct 09 2017
REFERENCES
Marc LeBrun, personal communication.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
M. F. Hasler, Table of n, a(n) for n = 0..500 (first 200 terms from Sean A. Irvine)
A. J. Macfarlane, Generating functions for integer sequences defined by the evolution of cellular automata..., Fig 15.
Eric Weisstein's World of Mathematics, Cellular Automaton.
FORMULA
Numbers suggest a rational g.f. with denominator (1-x^4)(1-4x^2). - Ralf Stephan, Jun 09 2005
G.f. seems to be (1 + 3*x + x^2 + 3*x^3 + 2*x^4 - 4*x^5)/((1 - x^4)*(1 - 4*x^2)). - Vincenzo Librandi, Sep 11 2017
EXAMPLE
n | a(n) [binary] | a(n) [decimal]
0 | ...01(0...) | 1
1 | ...011(0...) | 3 (From ...010.., using 001 -> 1, 010 -> 1, 100 -> 0)
2 | ...0101(0...) | 5 (001 -> 1, 011 -> 0, 110 -> 1, 100 -> 0)
3 | ...01111(0...) | 15 (001 -> 1, 010 -> 1, 101 -> 1, 110 -> 1, 100 -> 0)
4 | ...010111(0...) | 23 (001 -> 1, 011 -> 0, 111 -> 1, 110 -> 1)
5 | ...0111011(0...) | 59 (patterns of both of the above combined)
6 |...01011101(0...) | 93 (as above)
MATHEMATICA
FromDigits[#, 2] & /@ CellularAutomaton[230, {{1}, 0}, 32] (* Michael De Vlieger, Oct 09 2017 *)
PROG
(PARI) vector(90, i, a=if(i>1, A292682(a), 1))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Edited by M. F. Hasler, Oct 09 2017
STATUS
approved