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Total number of OFF (white) cells after n iterations of the "Rule 129" elementary cellular automaton starting with a single ON (black) cell.
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%I #7 Jan 16 2016 10:34:04

%S 0,3,7,14,18,26,34,49,53,61,69,85,93,109,125,156,160,168,176,192,200,

%T 216,232,264,272,288,304,336,352,384,416,479,483,491,499,515,523,539,

%U 555,587,595,611,627,659,675,707,739,803,811,827,843,875,891,923,955

%N Total number of OFF (white) cells after n iterations of the "Rule 129" elementary cellular automaton starting with a single ON (black) cell.

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

%H Robert Price, <a href="/A267448/b267448.txt">Table of n, a(n) for n = 0..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://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="/index/Ce#cell">Index entries for sequences related to cellular automata</a>

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

%t 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 *) nbc=Table[Total[catri[[k]]],{k,1,rows}]; (* Number of Black cells in stage n *) nwc=Table[Length[catri[[k]]]-nbc[[k]],{k,1,rows}]; (* Number of White cells in stage n *) Table[Total[Take[nwc,k]],{k,1,rows}] (* Number of White cells through stage n *)

%Y Cf. A267417.

%K nonn,easy

%O 0,2

%A _Robert Price_, Jan 15 2016