A006977 Cellular automaton with Rule 230: 000, 001, 010, 011, ..., 111 -> 0,1,1,0,0,1,1,1. (Formerly M2497)

1, 3, 5, 15, 23, 59, 93, 239, 375, 955, 1501, 3823, 6007, 15291, 24029, 61167, 96119, 244667, 384477, 978671, 1537911, 3914683, 6151645, 15658735, 24606583, 62634939, 98426333, 250539759, 393705335, 1002159035, 1574821341, 4008636143, 6299285367

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.

Index entries for sequences related to cellular automata

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

Cf. A292682; A292680, A292681, A266178, A266179, A266180; ...

Sequence in context: A329852 A283908 A284409 * A284481 A290662 A003549

Adjacent sequences: A006974 A006975 A006976 * A006978 A006979 A006980

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Edited by M. F. Hasler, Oct 09 2017

Status

approved