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%I #19 Sep 21 2017 11:59:11
%S 1,6,22,90,358,1434,5734,22938,91750,367002,1468006,5872026,23488102,
%T 93952410,375809638,1503238554,6012954214,24051816858,96207267430,
%U 384829069722,1539316278886,6157265115546,24629060462182,98516241848730,394064967394918,1576259869579674
%N a(n) = A255464(2^n-1).
%H Colin Barker, <a href="/A255465/b255465.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_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,4).
%F G.f.: (1+3*x) / ((1+x)*(1-4*x)).
%F From _Colin Barker_, Feb 04 2017: (Start)
%F a(n) = (-2*(-1)^n + 7*4^n) / 5.
%F a(n) = 3*a(n-1) + 4*a(n-2) for n>1.
%F (End)
%t LinearRecurrence[{3, 4}, {1, 6}, 26] (* _Jean-François Alcover_, Sep 21 2017 *)
%o (PARI) Vec((1+3*x) / ((1+x)*(1-4*x)) + O(x^30)) \\ _Colin Barker_, Feb 04 2017
%Y Cf. A255464.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_ and _Doron Zeilberger_, Feb 23 2015
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