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A071028 Triangle read by rows giving successive states of cellular automaton generated by "Rule 50". 9
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, 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

Index to Elementary Cellular Auto

Index entries for sequences related to cellular automata

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

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: A054521 A014240 A014471 * A011635 A015752 A015878

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 March 25 19:30 EDT 2017. Contains 284082 sequences.