A071035 - OEIS

%I #38 Feb 16 2025 08:32:46

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

%C Row n has length 2n+1.

%D S. Wolfram, A New Kind of Science, Wolfram Media, 2002; Chapter 3.

%H Robert Price, <a href="/A071035/b071035.txt">Table of n, a(n) for n = 0..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>

%H S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>

%H <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>

%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>

%e Triangle begins:

%e                            1,

%e                         1, 1, 1,

%e                      1, 1, 0, 1, 1,

%e                   1, 1, 1, 1, 1, 1, 1,

%e                1, 1, 0, 0, 0, 0, 0, 1, 1,

%e             1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1,

%e          1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1,

%e       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,

%e    1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1,

%e 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1,

%e ... - _N. J. A. Sloane_, Aug 24 2014

%t A071035list[rowmax_]:=MapIndexed[ArrayPad[#1, #2-rowmax-1]&,CellularAutomaton[126,{{1},0},rowmax]];A071035list[10] (* Generates 11 rows *) (* _Paolo Xausa_, Jul 18 2023 *)

%Y See A071051 for number of ON states.

%Y The right half is the triangle A127872.

%Y Cf. A036987 (central column).

%K nonn,tabf,changed

%O 0,1

%A _Hans Havermann_, May 26 2002

%E Corrected by _Hans Havermann_, Jan 07 2012