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

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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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

Examples

			   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)
		

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

Crossrefs

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

Programs

Mathematica

FromDigits[#, 2] & /@ CellularAutomaton[230, {{1}, 0}, 32] (* Michael De Vlieger, Oct 09 2017 *)

PARI

vector(90,i,a=if(i>1,A292682(a),1))

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

Extensions

Edited by M. F. Hasler, Oct 09 2017