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

%I A006977 M2497 #50 Feb 16 2025 08:32:31
%S A006977 1,3,5,15,23,59,93,239,375,955,1501,3823,6007,15291,24029,61167,96119,
%T A006977 244667,384477,978671,1537911,3914683,6151645,15658735,24606583,
%U A006977 62634939,98426333,250539759,393705335,1002159035,1574821341,4008636143,6299285367
%N A006977 Cellular automaton with Rule 230: 000, 001, 010, 011, ..., 111 -> 0,1,1,0,0,1,1,1.
%C A006977 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
%D A006977 _Marc LeBrun_, personal communication.
%D A006977 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A006977 M. F. Hasler, <a href="/A006977/b006977.txt">Table of n, a(n) for n = 0..500</a> (first 200 terms from Sean A. Irvine)
%H A006977 A. J. Macfarlane, <a href="http://www.damtp.cam.ac.uk/user/ajm/Papers2016/GFsForCAsOfEvenRuleNo.ps">Generating functions for integer sequences defined by the evolution of cellular automata...</a>, Fig 15.
%H A006977 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CellularAutomaton.html">Cellular Automaton</a>.
%H A006977 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%F A006977 Numbers suggest a rational g.f. with denominator (1-x^4)(1-4x^2). - _Ralf Stephan_, Jun 09 2005
%F A006977 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
%e A006977    n  |    a(n) [binary] | a(n) [decimal]
%e A006977    0  |      ...01(0...) |   1
%e A006977    1  |     ...011(0...) |   3   (From ...010.., using 001 -> 1, 010 -> 1, 100 -> 0)
%e A006977    2  |    ...0101(0...) |   5   (001 -> 1, 011 -> 0, 110 -> 1, 100 -> 0)
%e A006977    3  |   ...01111(0...) |  15   (001 -> 1, 010 -> 1, 101 -> 1, 110 -> 1, 100 -> 0)
%e A006977    4  |  ...010111(0...) |  23   (001 -> 1, 011 -> 0, 111 -> 1, 110 -> 1)
%e A006977    5  | ...0111011(0...) |  59   (patterns of both of the above combined)
%e A006977    6  |...01011101(0...) |  93   (as above)
%t A006977 FromDigits[#, 2] & /@ CellularAutomaton[230, {{1}, 0}, 32] (* _Michael De Vlieger_, Oct 09 2017 *)
%o A006977 (PARI) vector(90,i,a=if(i>1,A292682(a),1))
%Y A006977 Cf. A292682; A292680, A292681, A266178, A266179, A266180; ...
%K A006977 nonn,easy
%O A006977 0,2
%A A006977 _N. J. A. Sloane_
%E A006977 Edited by _M. F. Hasler_, Oct 09 2017