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A006977 Cellular automaton with Rule 230: 000, 001, 010, 011, ..., 111 -> 0,1,1,0,0,1,1,1.
(Formerly M2497)
5

%I M2497 #49 Oct 29 2023 21:20:04

%S 1,3,5,15,23,59,93,239,375,955,1501,3823,6007,15291,24029,61167,96119,

%T 244667,384477,978671,1537911,3914683,6151645,15658735,24606583,

%U 62634939,98426333,250539759,393705335,1002159035,1574821341,4008636143,6299285367

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

%C 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 _Marc LeBrun_, personal communication.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H 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 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CellularAutomaton.html">Cellular Automaton</a>.

%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>

%F Numbers suggest a rational g.f. with denominator (1-x^4)(1-4x^2). - _Ralf Stephan_, Jun 09 2005

%F 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 n | a(n) [binary] | a(n) [decimal]

%e 0 | ...01(0...) | 1

%e 1 | ...011(0...) | 3 (From ...010.., using 001 -> 1, 010 -> 1, 100 -> 0)

%e 2 | ...0101(0...) | 5 (001 -> 1, 011 -> 0, 110 -> 1, 100 -> 0)

%e 3 | ...01111(0...) | 15 (001 -> 1, 010 -> 1, 101 -> 1, 110 -> 1, 100 -> 0)

%e 4 | ...010111(0...) | 23 (001 -> 1, 011 -> 0, 111 -> 1, 110 -> 1)

%e 5 | ...0111011(0...) | 59 (patterns of both of the above combined)

%e 6 |...01011101(0...) | 93 (as above)

%t FromDigits[#, 2] & /@ CellularAutomaton[230, {{1}, 0}, 32] (* _Michael De Vlieger_, Oct 09 2017 *)

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

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

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_

%E Edited by _M. F. Hasler_, Oct 09 2017

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Last modified March 28 16:00 EDT 2024. Contains 371254 sequences. (Running on oeis4.)