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 A267679 Triangle read by rows giving successive states of cellular automaton generated by "Rule 201" initiated with a single ON (black) cell. 4
 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0 COMMENTS Row n has length 2n+1. The fact that only n cells to the left and right of the initially active cell are updated at step n is contradictory to the usual treatment of a "Rule m" automaton, where all cells are updated depending on their neighborhood. See also the illustration of "Rule 201" on the MathWorld page. - M. F. Hasler, Jul 28 2018 REFERENCES S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55. LINKS Robert Price, Table of n, a(n) for n = 0..10000 Eric Weisstein's World of Mathematics, Elementary Cellular Automaton S. Wolfram, A New Kind of Science EXAMPLE The first ten rows:                   1                 0 0 0               1 0 1 0 1             1 1 0 0 0 1 1           1 1 1 0 1 0 1 1 1         1 1 1 1 0 0 0 1 1 1 1       1 1 1 1 1 0 1 0 1 1 1 1 1     1 1 1 1 1 1 0 0 0 1 1 1 1 1 1   1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 MATHEMATICA rule=201; rows=20; ca=CellularAutomaton[rule, {{1}, 0}, rows-1, {All, All}]; (* Start with single black cell *) catri=Table[Take[ca[[k]], {rows-k+1, rows+k-1}], {k, 1, rows}]; (* Truncated list of each row *) Flatten[catri] (* Triangle Representation of CA *) PROG (PARI) A267679_row(n)=if(n==1, [0, 0, 0], binary(1<<(n*2+1)-(bittest(n, 0)*2+5)<<(n-1)-1)) \\ M. F. Hasler, Jul 28 2018 CROSSREFS Cf. A267681 (value of row n read as binary number). - M. F. Hasler, Jul 28 2018 Sequence in context: A089011 A267043 A266444 * A267868 A288733 A095111 Adjacent sequences:  A267676 A267677 A267678 * A267680 A267681 A267682 KEYWORD nonn,tabf,easy AUTHOR Robert Price, Jan 19 2016 STATUS approved

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Last modified January 26 01:48 EST 2020. Contains 331270 sequences. (Running on oeis4.)