cp's OEIS Frontend

A246038 G.f.: (1+2x)(1+2x+4x^2)/(1-3x-8x^3-8x^4).

%I A246038 #15 Mar 03 2024 18:59:46
%S A246038 1,7,29,103,373,1407,5277,19639,73157,272943,1018157,3796839,14159317,
%T A246038 52806751,196940221,734469911,2739138277,10215390607,38097452877,
%U A246038 142081224135,529879903477,1976142458303,7369856791005,27485259393911,102503957075973,382279865222383,1425680525146477,5316955307198503
%N A246038 G.f.: (1+2x)(1+2x+4x^2)/(1-3x-8x^3-8x^4).
%C A246038 This is the subsequence A246039(2^n-1), n >= 0.
%H A246038 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, 2015; see also the <a href="http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/CAcount.html">Accompanying Maple Package</a>.
%H A246038 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, 2015.
%H A246038 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 A246038 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, 2015
%H A246038 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A246038 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3, 0, 8, 8).
%p A246038 -(2*x+1)*(4*x^2+2*x+1)/(8*x^4+8*x^3+3*x-1);
%t A246038 LinearRecurrence[{3, 0, 8, 8}, {1, 7, 29, 103}, 28] (* _Jean-François Alcover_, Oct 09 2018 *)
%Y A246038 Cf. A246039.
%K A246038 nonn
%O A246038 0,2
%A A246038 _N. J. A. Sloane_, Aug 21 2014