A075437 Triangle read by rows giving successive iterations of the Rule 110 elementary cellular automaton starting with a single black (1) cell where row n is of length 2n+1.

1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1

Offset

0,1

Comments

The right n terms in a(n) are all 0.

T(n,k) = A070887(n+1,k+1), k=0..n. - Reinhard Zumkeller, Jun 26 2013

References

S. Wolfram, A New Kind of Science. Champaign, IL: Wolfram Media, p. 31ff, 2002.

Links

Reinhard Zumkeller, Rows n = 0..100 of triangle, flattened

Eric Weisstein's World of Mathematics, Rule 110

S. Wolfram, A New Kind of Science

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Example

      1;
    1,1,0;
  1,1,1,0,0;
1,1,0,1,0,0,0; ...

Mathematica

A075437list[rowmax_]:=MapIndexed[ArrayPad[#1, #2-rowmax-1]&, CellularAutomaton[110, {{1}, 0}, {rowmax, All}]]; A075437list[10] (* Generates 11 rows *) (* Paolo Xausa, Oct 04 2023 *)

Prog

(Haskell)
a075437 n k = a075437_tabf !! n !! k
a075437_row n = a075437_tabf !! n
a075437_tabf = iterate rule110 [1] where
   rule110 row = f ([0, 0] ++ row ++ [0, 0]) where
       f [_, _]          = []
       f (_:ws@(0:0:_)) = 0 : f ws
       f (1:ws@(1:1:_)) = 0 : f ws
       f (_:ws@(_:_:_)) = 1 : f ws
-- Reinhard Zumkeller, Jun 26 2013

Crossrefs

Cf. A070887.

Sequence in context: A342005 A354355 A266974 * A130047 A293233 A302050

Adjacent sequences: A075434 A075435 A075436 * A075438 A075439 A075440

Keyword

nonn,tabf

Author

Eric W. Weisstein, Sep 15 2002

Status

approved