A255457 - OEIS

%I #15 Jan 09 2019 03:54:13

%S 1,5,23,93,359,1335,4873,17535,62601,222181,785855,2772717,9768351,

%T 34378167,120910529,425062511,1493898001,5249371781,18443445415,

%U 64795091709,227625068503,799619495287,2808906276921,9866994688223,34659998140825,121750158651877,427670046315727,1502266603229837,5276968090316303

%N a(n) = A255456(2^n-1).

%H Colin Barker, <a href="/A255457/b255457.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_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,0,-24,15,17).

%F G.f.: (1-x)*(1+x-x^2+x^3) / (1-5*x+24*x^3-15*x^4-17*x^5).

%F a(n) = 5*a(n-1) - 24*a(n-3) + 15*a(n-4) + 17*a(n-5) for n>4. - _Colin Barker_, Feb 03 2017

%t LinearRecurrence[{5, 0, -24, 15, 17}, {1, 5, 23, 93, 359}, 30] (* _Jean-François Alcover_, Jan 09 2019 *)

%o (PARI) Vec((1-x)*(1+x-x^2+x^3) / (1-5*x+24*x^3-15*x^4-17*x^5) + O(x^30)) \\ _Colin Barker_, Feb 03 2017

%Y Cf. A255456.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_ and _Doron Zeilberger_, Feb 23 2015