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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
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
Michael Williams, Collatz conjecture: an order isomorphic recursive machine, ResearchGate (2024). See pp. 8, 13.
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
KEYWORD
nonn,tabf
AUTHOR
Hans Havermann, May 26 2002
STATUS
approved

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Last modified March 29 04:59 EDT 2024. Contains 371264 sequences. (Running on oeis4.)