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 A071028 Triangle read by rows giving successive states of cellular automaton generated by "Rule 50". 10
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Row n has length 2n+1. Rules #50, #58, #114, #122, #178, #179, #186, #242, #250 all give rise to this sequence. The following sequences all have the same parity: A004737, A006590, A027052, A071028, A071797, A078358, A078446. - Jeremy Gardiner, Mar 16 2003 REFERENCES S. Wolfram, A New Kind of Science, Wolfram Media, 2002; Chapter 3. LINKS Robert Price, Table of n, a(n) for n = 0..9999 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 S. Wolfram, A New Kind of Science FORMULA 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) = A071797(n) (mod 2). - Boris Putievskiy, Jul 24 2013 a(n) = (1+(-1)^(Sum_{k=1..floor(n/2)} floor((n-k)/k)))/2. - Wesley Ivan Hurt, Dec 25 2020 EXAMPLE 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; - Philippe Deléham, Mar 23 2014 MATHEMATICA 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 *) CROSSREFS Cf. A071797. Sequence in context: A014240 A014471 A230002 * A286987 A011635 A015752 Adjacent sequences: A071025 A071026 A071027 * A071029 A071030 A071031 KEYWORD nonn,tabf AUTHOR Hans Havermann, May 26 2002 STATUS approved

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Last modified December 1 12:40 EST 2022. Contains 358468 sequences. (Running on oeis4.)