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Total number of ON (black) cells after n iterations of the "Rule 45" elementary cellular automaton starting with a single ON (black) cell.
1

%I #6 Jan 02 2016 03:59:53

%S 1,2,6,8,13,20,28,36,43,56,65,77,88,106,121,139,153,176,192,214,229,

%T 259,282,305,325,361,379,409,441,471,501,535,563,600,633,677,704,756,

%U 781,834,866,913,951,1005,1033,1095,1131,1188,1226,1287,1330,1389,1428

%N Total number of ON (black) cells after n iterations of the "Rule 45" elementary cellular automaton starting with a single ON (black) cell.

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

%H G. C. Greubel, <a href="/A266627/b266627.txt">Table of n, a(n) for n = 0..2500</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=45; 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. A266619.

%K nonn,easy

%O 0,2

%A _Robert Price_, Jan 01 2016