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Total number of ON (black) cells after n iterations of the "Rule 167" elementary cellular automaton starting with a single ON (black) cell.
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%I #7 Jan 18 2016 02:06:57

%S 1,3,6,11,16,25,34,45,54,71,88,107,124,147,168,191,208,241,274,309,

%T 342,381,418,457,490,537,582,629,670,721,766,813,846,911,976,1043,

%U 1108,1179,1248,1319,1384,1463,1540,1619,1692,1775,1852,1931,1996,2091,2184

%N Total number of ON (black) cells after n iterations of the "Rule 167" 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="/A267583/b267583.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=167; 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 *) Table[Total[Take[nbc,k]],{k,1,rows}] (* Number of Black cells through stage n *)

%Y Cf. A267576.

%K nonn,easy

%O 0,2

%A _Robert Price_, Jan 17 2016