OFFSET
0,4
COMMENTS
Run length transform gives A246035. - N. J. A. Sloane, Feb 26 2015
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Shalosh B. Ekhad, N. J. A. Sloane, and Doron Zeilberger, A Meta-Algorithm for Creating Fast Algorithms for Counting ON Cells in Odd-Rule Cellular Automata, arXiv:1503.01796 [math.CO], 2015; see also the Accompanying Maple Package.
Shalosh B. Ekhad, N. J. A. Sloane, and Doron Zeilberger, Odd-Rule Cellular Automata on the Square Grid, arXiv:1503.04249, 2015.
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: Part 1, Part 2
N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015.
Index entries for linear recurrences with constant coefficients, signature (3,6,-8).
FORMULA
a(n) = 3*a(n-1) + 6*a(n-2) - 8*a(n-3).
a(n) = (A001045(n))^2.
G.f.: x*(1-2*x)/((1-x)*(1+2*x)*(1-4*x)).
MATHEMATICA
LinearRecurrence[{3, 6, -8}, {0, 1, 1}, 25] (* Jean-François Alcover, Jan 09 2019 *)
PROG
(Magma) [1/9-(2/9)*(-2)^n+(1/9)*4^n: n in [0..35]]; // Vincenzo Librandi, Aug 09 2011
(PARI) concat (0, Vec(x*(1-2*x)/((1-x)*(1+2*x)*(1-4*x)) + O(x^30))) \\ Michel Marcus, Mar 04 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, May 17 2008
EXTENSIONS
More terms from R. J. Mathar, Dec 12 2009
STATUS
approved