%I #12 Sep 15 2018 05:29:26
%S 1,5,5,19,5,25,19,71,5,25,25,95,19,95,71,265,5,25,25,95,25,125,95,355,
%T 19,95,95,361,71,355,265,989,5,25,25,95,25,125,95,355,25,125,125,475,
%U 95,475,355,1325,19,95,95,361,95,475,361,1349,71,355,355,1349
%N Number of ON cells after n generations of the odd-rule cellular automaton defined by OddRule 037 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 [math.CO], 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>
%t (* b = a1834 *) b[0] = 1; b[1] = 5; b[n_] := b[n] = 4 b[n-1] - b[n-2];
%t Table[Times @@ (b[Length[#]]&) /@ Select[Split[IntegerDigits[n, 2]], #[[1]] == 1&], {n, 0, 59}] (* _Jean-François Alcover_, Sep 15 2018 *)
%Y Run length transform of A001834.
%K nonn
%O 0,2
%A _N. J. A. Sloane_ and _Doron Zeilberger_, Feb 23 2015