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A071035 Triangle read by rows giving successive states of cellular automaton generated by "Rule 126".

%I A071035 #38 Feb 16 2025 08:32:46
%S A071035 1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,0,0,0,1,1,
%T A071035 1,1,1,1,0,0,1,1,0,1,1,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,
%U A071035 0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1
%N A071035 Triangle read by rows giving successive states of cellular automaton generated by "Rule 126".
%C A071035 Row n has length 2n+1.
%D A071035 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; Chapter 3.
%H A071035 Robert Price, <a href="/A071035/b071035.txt">Table of n, a(n) for n = 0..10000</a>
%H A071035 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A071035 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A071035 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%H A071035 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%e A071035 Triangle begins:
%e A071035                            1,
%e A071035                         1, 1, 1,
%e A071035                      1, 1, 0, 1, 1,
%e A071035                   1, 1, 1, 1, 1, 1, 1,
%e A071035                1, 1, 0, 0, 0, 0, 0, 1, 1,
%e A071035             1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1,
%e A071035          1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1,
%e A071035       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
%e A071035    1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1,
%e A071035 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1,
%e A071035 ... - _N. J. A. Sloane_, Aug 24 2014
%t A071035 A071035list[rowmax_]:=MapIndexed[ArrayPad[#1, #2-rowmax-1]&,CellularAutomaton[126,{{1},0},rowmax]];A071035list[10] (* Generates 11 rows *) (* _Paolo Xausa_, Jul 18 2023 *)
%Y A071035 See A071051 for number of ON states.
%Y A071035 The right half is the triangle A127872.
%Y A071035 Cf. A036987 (central column).
%K A071035 nonn,tabf
%O A071035 0,1
%A A071035 _Hans Havermann_, May 26 2002
%E A071035 Corrected by _Hans Havermann_, Jan 07 2012