%I #12 Feb 05 2017 04:41:51
%S 1,6,24,100,396,1596,6364,25500,101916,407836,1631004,6524700,
%T 26097436,104392476,417564444,1670268700,6681052956,26724255516,
%U 106896934684,427587913500,1710351304476,6841405916956,27365622269724,109462491875100,437849961907996,1751399858816796,7005599412897564,28022397696329500,112089590695839516
%N a(n) = A255470(2^n-1).
%H Colin Barker, <a href="/A255471/b255471.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 (3,6,-8).
%F G.f.: (1+3*x)/((1-x)*(1+2*x)*(1-4*x)).
%F From _Colin Barker_, Feb 04 2017: (Start)
%F a(n) = (-4 - (-2)^n + 7*2^(1+2*n)) / 9.
%F a(n) = 3*a(n-1) + 6*a(n-2) - 8*a(n-3) for n>2.
%F (End)
%o (PARI) Vec((1+3*x) / ((1-x)*(1+2*x)*(1-4*x)) + O(x^30)) \\ _Colin Barker_, Feb 04 2017
%Y Cf. A255470.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_ and _Doron Zeilberger_, Feb 23 2015