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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.

%I A075437 #26 Feb 16 2025 08:32:47
%S A075437 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,
%T A075437 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,
%U A075437 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
%N 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.
%C A075437 The right n terms in a(n) are all 0.
%C A075437 T(n,k) = A070887(n+1,k+1), k=0..n. - _Reinhard Zumkeller_, Jun 26 2013
%D A075437 S. Wolfram, A New Kind of Science. Champaign, IL: Wolfram Media, p. 31ff, 2002.
%H A075437 Reinhard Zumkeller, <a href="/A075437/b075437.txt">Rows n = 0..100 of triangle, flattened</a>
%H A075437 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Rule110.html">Rule 110</a>
%H A075437 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A075437 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A075437 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%e A075437       1;
%e A075437     1,1,0;
%e A075437   1,1,1,0,0;
%e A075437 1,1,0,1,0,0,0; ...
%t A075437 A075437list[rowmax_]:=MapIndexed[ArrayPad[#1,#2-rowmax-1]&,CellularAutomaton[110,{{1},0},{rowmax,All}]];A075437list[10] (* Generates 11 rows *) (* _Paolo Xausa_, Oct 04 2023 *)
%o A075437 (Haskell)
%o A075437 a075437 n k = a075437_tabf !! n !! k
%o A075437 a075437_row n = a075437_tabf !! n
%o A075437 a075437_tabf = iterate rule110 [1] where
%o A075437    rule110 row = f ([0,0] ++ row ++ [0,0]) where
%o A075437        f [_,_]          = []
%o A075437        f (_:ws@(0:0:_)) = 0 : f ws
%o A075437        f (1:ws@(1:1:_)) = 0 : f ws
%o A075437        f (_:ws@(_:_:_)) = 1 : f ws
%o A075437 -- _Reinhard Zumkeller_, Jun 26 2013
%Y A075437 Cf. A070887.
%K A075437 nonn,tabf
%O A075437 0,1
%A A075437 _Eric W. Weisstein_, Sep 15 2002