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%I #14 Sep 30 2016 13:09:22
%S 1,4,16,58,204,714,2492,8682,30228,105226,366276,1274922,4437692,
%T 15446554,53765916,187147146,651418116,2267444842,7892485300,
%U 27472040138,95624259340,332847482970,1158570537292,4032735032490,14037083980308,48860072772074,170071413502180,591982043090090,2060562279111580,7172374493538586,24965494321148156,86899520830961866,302478557946941732,1052862859805769450,3664789362535367700
%N A255298(2^n-1).
%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>
%F G.f.: (1-x)*(1-x+x^2-x^3-4*x^4+2*x^5-2*x^6)/(1-6*x+10*x^2-4*x^3-3*x^4+12*x^5-20*x^6+10*x^7-4*x^8).
%t A255299[n_] := SeriesCoefficient[(1 - x)*(1 - x + x^2 - x^3 - 4*x^4 + 2*x^5 - 2*x^6)/(1 - 6*x + 10*x^2 - 4*x^3 - 3*x^4 + 12*x^5 - 20*x^6 + 10*x^7 - 4*x^8), {x, 0, n}]; Array[A255299, 35, 0] (* _JungHwan Min_, Sep 29 2016 *)
%t A255299L[n_] := CoefficientList[Series[(1 - x)*(1 - x + x^2 - x^3 - 4*x^4 + 2*x^5 - 2*x^6)/(1 - 6*x + 10*x^2 - 4*x^3 - 3*x^4 + 12*x^5 - 20*x^6 + 10*x^7 - 4*x^8), {x, 0, n}], x]; A255299L[34] (* _JungHwan Min_, Sep 29 2016 *)
%Y Cf. A255298.
%K nonn
%O 0,2
%A _N. J. A. Sloane_ and _Doron Zeilberger_, Feb 23 2015
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