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A071032 Triangle read by rows giving successive states of cellular automaton generated by "Rule 86".

%I A071032 #29 Feb 16 2025 08:32:46
%S A071032 1,1,1,1,1,0,0,1,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,1,1,1,1,1,0,1,1,1,1,0,
%T A071032 1,1,1,0,0,1,0,0,0,0,1,0,0,1,1,1,1,1,1,1,1,0,0,1,1,1,1,0,1,1,1,0,0,0,
%U A071032 0,0,1,1,1,0,0,0,1,0,0,1,1,1,1,1,0,0,0,1,0,0,1,1,0,1,1,1,1,0,1
%N A071032 Triangle read by rows giving successive states of cellular automaton generated by "Rule 86".
%C A071032 Row n has length 2n+1.
%D A071032 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; Chapter 3.
%H A071032 Reinhard Zumkeller, <a href="/A071032/b071032.txt">Rows n = 0..120 of triangle, flattened</a>
%H A071032 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Rule30.html">Rule 30</a>
%H A071032 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A071032 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%H A071032 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%F A071032 T(n,k) = A070950(n,2*n+1-k), 0 <= k <= 2*n+1. - _Reinhard Zumkeller_, Jun 08 2013
%t A071032 A071032list[rowmax_]:=MapIndexed[ArrayPad[#1,#2-rowmax-1]&,CellularAutomaton[86,{{1},0},rowmax]];A071032list[10] (* Generates 11 rows *) (* _Paolo Xausa_, Jun 01 2023 *)
%o A071032 (Haskell)
%o A071032 a071032 n k = a071032_tabf !! n !! k
%o A071032 a071032_row n = a071032_tabf !! n
%o A071032 a071032_tabf = map reverse a070950_tabf
%o A071032 -- _Reinhard Zumkeller_, Jun 08 2013
%Y A071032 Cf. A005408 (row lengths), A070952 (row sums), A051023 (central terms), A070950 (mirror image, rule 30), A226464 (complemented, rule 149).
%K A071032 nonn,tabf
%O A071032 0,1
%A A071032 _Hans Havermann_, May 26 2002
%E A071032 Corrected by _Hans Havermann_, Jan 07 2012