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 A267708 Triangle read by rows giving successive states of cellular automaton generated by "Rule 206" initiated with a single ON (black) cell. 1
 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0 COMMENTS Row n has length 2n+1. This sequence is also generated by Rule 238. 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 FORMULA Conjecture: a(n) = (1 + (-1)^floor(2*sqrt(n)))/2. - Velin Yanev, Nov 30 2016 EXAMPLE The first ten rows:                   1                 1 1 0               1 1 1 0 0             1 1 1 1 0 0 0           1 1 1 1 1 0 0 0 0         1 1 1 1 1 1 0 0 0 0 0       1 1 1 1 1 1 1 0 0 0 0 0 0     1 1 1 1 1 1 1 1 0 0 0 0 0 0 0   1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 MATHEMATICA rule=206; 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 *) CROSSREFS Sequence in context: A060038 A197774 A219009 * A167021 A267687 A304653 Adjacent sequences:  A267705 A267706 A267707 * A267709 A267710 A267711 KEYWORD nonn,tabf,easy AUTHOR Robert Price, Jan 19 2016 STATUS approved

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Last modified August 6 15:36 EDT 2020. Contains 336252 sequences. (Running on oeis4.)