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%I #14 Jul 20 2018 11:26:16
%S 1,7,31,145,601,2551,10351,42433,170761,690247,2768191,11123185,
%T 44543161,178525591,714455311,2860291873,11443638121,45791846887,
%U 183184681951,732859788625,2931560215321,11727088287031,46909200573871,187642734275713,750576869083081
%N a(n) = A255283(2^n-1).
%H Colin Barker, <a href="/A255284/b255284.txt">Table of n, a(n) for n = 0..1000</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_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,7,-28).
%F G.f.: (1 - x)*(1 + 4*x) / ((1 - 4*x)*(1 - 7*x^2)).
%F From _Colin Barker_, Feb 04 2017: (Start)
%F a(n) = 2^(3+2*n)/3 - 7^((n-1)/2)/6*(11-11*(-1)^n + 5*sqrt(7) + 5*(-1)^n*sqrt(7)).
%F a(n) = 4*a(n-1) + 7*a(n-2) - 28*a(n-3) for n>2.
%F (End)
%t LinearRecurrence[{4,7,-28},{1,7,31},30] (* _Harvey P. Dale_, Jul 20 2018 *)
%o (PARI) Vec((1 - x)*(1 + 4*x) / ((1 - 4*x)*(1 - 7*x^2)) + O(x^30)) \\ _Colin Barker_, Feb 04 2017
%Y Cf. A255283.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_ and _Doron Zeilberger_, Feb 19 2015
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