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Robert Price, <a href="/A267126/b267126.txt">Table of n, a(n) for n = 0..10000</a>

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The first ten rows: 1 1 0 0 0 1 0 1 0 1 1 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1 0 0 0 1 1 0 1 0 0 1 0 0 0 1 1 1 1 0 1 1 0 0 1 0 0 1 1 1 0 0 0 0 1 1 0 1 0 1 0 0 1 0 0 0 0 1 1 1 1 1 0 1 1 0 1 0 0 1 0 0 1 1 1 1

The first ten rows:

1

1 0 0

0 1 0 1 0

1 1 0 1 0 0 1

0 0 1 1 0 0 1 0 0

1 1 1 0 1 0 1 0 0 1 1

0 0 0 1 1 0 1 0 0 1 0 0 0

1 1 1 1 0 1 1 0 0 1 0 0 1 1 1

0 0 0 0 1 1 0 1 0 1 0 0 1 0 0 0 0

1 1 1 1 1 0 1 1 0 1 0 0 1 0 0 1 1 1 1

allocated for Robert PriceTriangle read by rows giving successive states of cellular automaton generated by "Rule 99" initiated with a single ON (black) cell.

1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1

0

Row n has length 2n+1.

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

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

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

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

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

The first ten rows: 1 1 0 0 0 1 0 1 0 1 1 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1 0 0 0 1 1 0 1 0 0 1 0 0 0 1 1 1 1 0 1 1 0 0 1 0 0 1 1 1 0 0 0 0 1 1 0 1 0 1 0 0 1 0 0 0 0 1 1 1 1 1 0 1 1 0 1 0 0 1 0 0 1 1 1 1

rule=99; rows=20; ca=CellularAutomaton[rule, {{1}, 0}, rows-1, {All, All}]; (* Start with single black cell *) catri=Table[Take[ca[[k]], {rows-k+1, rows+k-1}], {k, 1, rows}]; (* Truncated list of each row *) Flatten[catri] (* Triangle Representation of CA *)

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nonn,tabf,easy

Robert Price, Jan 10 2016

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