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%I #27 Feb 13 2022 16:00:37
%S 1,4,16,60,216,768,2728,9704,34552,123064,438328,1561176,5560248,
%T 19803096,70529656,251194904,894643768,3186321112,11348251384,
%U 40417397400,143948695992,512680882776,1825940038264,6503181876248,23161425701176,82490640856024,293794773978616,1046365603664280
%N a(n) = A255302(2^n - 1).
%H Matthew House, <a href="/A255303/b255303.txt">Table of n, a(n) for n = 0..1803</a>
%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>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (5,-6,2,4).
%F G.f.: (1 - x + 2*x^2 + 2*x^3)/((1 - 3*x - 2*x^2)*(1 - 2*x + 2*x^2)).
%F a(n) = 5*a(n-1) - 6*a(n-2) + 2*a(n-3) + 4*a(n-4). - _Matthew House_, Jan 15 2017
%t A255303[n_] := SeriesCoefficient[(1 - x + 2*x^2 + 2*x^3)/((1 - 3*x - 2*x^2)*(1 - 2*x + 2*x^2)), {x, 0, n}]; Array[A255303, 28, 0] (* _JungHwan Min_, Sep 29 2016 *)
%t A255303L[n_] := CoefficientList[Series[(1 - x + 2*x^2 + 2*x^3)/((1 - 3*x - 2*x^2)*(1 - 2*x + 2*x^2)), {x, 0, n}], x]; A255303L[27] (* _JungHwan Min_, Sep 29 2016 *)
%t LinearRecurrence[{5,-6,2,4},{1,4,16,60},30] (* _Harvey P. Dale_, Feb 13 2022 *)
%Y Cf. A255302.
%K nonn
%O 0,2
%A _N. J. A. Sloane_ and _Doron Zeilberger_, Feb 23 2015
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