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Conjecture: a(n) = A071050(n), n>0. - R. J. Mathar, Jan 17 2016

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Robert Price, <a href="/A267445/b267445.txt">Table of n, a(n) for n = 0..1000</a>

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allocatedNumber of ON (black) cells in the n-th iteration of the "Rule 129" elementary cellular automaton starting with fora Robertsingle PriceON (black) cell.

1, 0, 1, 0, 5, 3, 5, 0, 13, 11, 13, 7, 17, 11, 13, 0, 29, 27, 29, 23, 33, 27, 29, 15, 41, 35, 37, 23, 41, 27, 29, 0, 61, 59, 61, 55, 65, 59, 61, 47, 73, 67, 69, 55, 73, 59, 61, 31, 89, 83, 85, 71, 89, 75, 77, 47, 97, 83, 85, 55, 89, 59, 61, 0, 125, 123, 125

0,5

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>

rule=129; 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 *) Table[Total[catri[[k]]], {k, 1, rows}] (* Number of Black cells in stage n *)

Cf. A267417.

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nonn,easy

Robert Price, Jan 15 2016

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