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A269174 Formula for Wolfram's Rule 124 cellular automaton: a(n) = (n OR 2n) AND ((n XOR 2n) OR (n XOR 4n)).

%I A269174 #31 Feb 16 2025 08:33:30
%S A269174 0,3,6,7,12,15,14,11,24,27,30,31,28,31,22,19,48,51,54,55,60,63,62,59,
%T A269174 56,59,62,63,44,47,38,35,96,99,102,103,108,111,110,107,120,123,126,
%U A269174 127,124,127,118,115,112,115,118,119,124,127,126,123,88,91,94,95,76,79,70,67,192,195,198,199,204,207,206,203,216
%N A269174 Formula for Wolfram's Rule 124 cellular automaton: a(n) = (n OR 2n) AND ((n XOR 2n) OR (n XOR 4n)).
%H A269174 Antti Karttunen, <a href="/A269174/b269174.txt">Table of n, a(n) for n = 0..32767</a>
%H A269174 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A269174 Stephen Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A269174 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A269174 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%F A269174 a(n) = A163617(n) AND A269173(n).
%F A269174 a(n) = A163617(n) AND (A048724(n) OR A048725(n)).
%F A269174 a(n) = (n OR 2n) AND ((n XOR 2n) OR (n XOR 4n)).
%F A269174 Other identities. For all n >= 0:
%F A269174 a(2*n) = 2*a(n).
%F A269174 a(n) = A057889(A161903(A057889(n))). [Rule 124 is the mirror image of rule 110.]
%F A269174 G.f.: (-3*x^3 - 2*x^2 - 3*x)/(x^4 - 1) + Sum_{k>=1}((2^(k + 1)*x^(2^k) - 2^(k + 1)*x^(14*2^(k - 2)))/((x^(2^(k + 2)) - 1)*(x - 1))). - _Miles Wilson_, Jan 25 2025
%t A269174 a[n_] := BitAnd[BitOr[n, 2n], BitOr[BitXor[n, 2n], BitXor[n, 4n]]];
%t A269174 a /@ Range[0, 100] (* _Jean-François Alcover_, Feb 23 2020 *)
%o A269174 (Scheme) (define (A269174 n) (A004198bi (A163617 n) (A003986bi (A048724 n) (A048725 n))))
%o A269174 (Python) def a(n): return (n|2*n)&((n^(2*n))|(n^(4*n))) # _Indranil Ghosh_, Apr 19 2017
%o A269174 (Go)
%o A269174 package main
%o A269174 import "fmt"
%o A269174 func main() {
%o A269174     for n:=0; n<=100; n++{
%o A269174     fmt.Println((n|2*n)&((n^(2*n))|(n^(4*n))))}
%o A269174 } // _Indranil Ghosh_, Apr 19 2017
%Y A269174 Cf. A003986, A003987, A004198, A048724, A048725, A057889, A269173, A161903.
%Y A269174 Cf. A269175.
%Y A269174 Cf. A269176 (numbers not present in this sequence).
%Y A269174 Cf. A269177 (same sequence sorted into ascending order, duplicates removed).
%Y A269174 Cf. A269178 (numbers that occur only once).
%Y A269174 Cf. A267357 (iterates from 1 onward).
%K A269174 nonn
%O A269174 0,2
%A A269174 _Antti Karttunen_, Feb 22 2016