OFFSET
0,2
COMMENTS
Essentially 8 times A083424.
Equals A160239(2^n). - N. J. A. Sloane, Oct 04 2014
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 [math.CO], 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, 2015
N. J. A. Sloane, Illustration for a(4) = 416.
N. J. A. Sloane, Illustration for a(5) = 1728.
N. J. A. Sloane, Illustration for a(6) = 6784.
N. J. A. Sloane, Illustration for a(7) = 27392 (tiff).
N. J. A. Sloane, Illustration for a(7) = 27392 (png).
Index entries for linear recurrences with constant coefficients, signature (2,8).
FORMULA
MATHEMATICA
CoefficientList[Series[(1 + 6 x) / (1 - 2 x - 8 x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Feb 20 2015 *)
PROG
(Magma) I:=[1, 8]; [n le 2 select I[n] else 2*Self(n-1)+8*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Feb 20 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Aug 15 2014
STATUS
approved