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

Author

Eric W. Weisstein, Sep 15 2002

Keywords

• nonn
• tabf

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

Examples

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

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

Crossrefs

Cf. A070887.

Programs

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

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 *)