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%I #12 Sep 15 2018 05:29:18
%S 1,4,4,14,4,16,14,46,4,16,16,56,14,56,46,146,4,16,16,56,16,64,56,184,
%T 14,56,56,196,46,184,146,454,4,16,16,56,16,64,56,184,16,64,64,224,56,
%U 224,184,584,14,56,56,196,56,224,196,644,46,184,184,644
%N Number of ON cells after n generations of the odd-rule cellular automaton defined by OddRule 035 when started with a single ON cell.
%H Shalosh B. Ekhad, N. J. A. Sloane, and Doron Zeilberger, <a href="http://arxiv.org/abs/1503.01796">A Meta-Algorithm for Creating Fast Algorithms for Counting ON Cells in Odd-Rule Cellular Automata</a>, arXiv:1503.01796 [math.CO], 2015; see also the <a href="http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/CAcount.html">Accompanying Maple Package</a>.
%H Shalosh B. Ekhad, N. J. A. Sloane, and Doron Zeilberger, <a href="http://arxiv.org/abs/1503.04249">Odd-Rule Cellular Automata on the Square Grid</a>, arXiv:1503.04249, 2015.
%H N. J. A. Sloane, On the No. of ON Cells in Cellular Automata, Video of talk in Doron Zeilberger's Experimental Math Seminar at Rutgers University, Feb. 05 2015: <a href="https://vimeo.com/119073818">Part 1</a>, <a href="https://vimeo.com/119073819">Part 2</a>
%H N. J. A. Sloane, <a href="http://arxiv.org/abs/1503.01168">On the Number of ON Cells in Cellular Automata</a>, arXiv:1503.01168 [math.CO], 2015.
%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%F Run length transform of A027649.
%t a27649[n_] := 2(3^n) - 2^n;
%t Table[Times @@ (a27649[Length[#]]&) /@ Select[Split[IntegerDigits[n, 2]], #[[1]] == 1&], {n, 0, 59}] (* _Jean-François Alcover_, Sep 15 2018 *)
%Y Cf. A027649.
%K nonn
%O 0,2
%A _N. J. A. Sloane_ and _Doron Zeilberger_, Feb 23 2015
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