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A071028
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Triangle read by rows giving successive states of cellular automaton generated by "Rule 50".
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10
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1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0
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OFFSET
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0,1
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COMMENTS
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Row n has length 2n+1.
Rules #50, #58, #114, #122, #178, #179, #186, #242, #250 all give rise to this sequence.
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REFERENCES
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S. Wolfram, A New Kind of Science, Wolfram Media, 2002; Chapter 3.
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LINKS
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C. J. Glasby, S. P. Glasby, and F. Pleijel, Worms by number, Proc. Roy. Soc. B, Proc. Biol. Sci. 275 (1647) (2008) 2071-2076.
Eric Weisstein's World of Mathematics, Rule 250
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FORMULA
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a(n) = n - 1 + floor(sqrt(n)) - 2*Sum_{k=1..n-1} a(k) for n >= 1. - Benoit Cloitre, Jan 24 2013
a(n) = (1+(-1)^(Sum_{k=1..floor(n/2)} floor((n-k)/k)))/2. - Wesley Ivan Hurt, Dec 25 2020
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EXAMPLE
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Triangle begins:
1;
1, 0, 1;
1, 0, 1, 0, 1;
1, 0, 1, 0, 1, 0, 1;
1, 0, 1, 0, 1, 0, 1, 0, 1;
1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1;
1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1;
1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1;
1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1;
1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1;
1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1;
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MATHEMATICA
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rows = 10; ca = CellularAutomaton[50, {{1}, 0}, rows-1]; Flatten[ Table[ca[[k, rows-k+1 ;; rows+k-1]], {k, 1, rows}]] (* Jean-François Alcover, May 24 2012 *)
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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