A267151 - OEIS

%I #7 Jan 12 2016 00:05:50

%S 0,3,5,10,16,25,33,44,58,67,79,94,114,129,147,168,198,207,235,250,282,

%T 309,339,372,416,431,469,494,540,573,613,656,718,727,787,802,866,893,

%U 955,988,1060,1087,1145,1190,1264,1309,1369,1432,1524,1539,1625,1650

%N Total number of OFF (white) cells after n iterations of the "Rule 105" 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="/A267151/b267151.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=105; 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. A267145.

%K nonn,easy

%O 0,2

%A _Robert Price_, Jan 11 2016