OFFSET
0,2
COMMENTS
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 [math.CO], 2015.
Index entries for linear recurrences with constant coefficients, signature (4).
FORMULA
a(n) = 4*a(n-1) for n > 1; a(0) = 1, a(1) = 6.
G.f.: (1+2*x)/(1-4*x).
a(n) = floor(6*4^(n-1)). - Karl V. Keller, Jr., Aug 30 2021
MATHEMATICA
a[n_]:=(MatrixPower[{{2, 2}, {2, 2}}, n].{{2}, {1}})[[2, 1]]; Table[a[n], {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 20 2010 *)
Join[{1}, (3*4^Range[25])/2] (* or *) Join[{1}, NestList[4#&, 6, 25]] (* Harvey P. Dale, Feb 14 2012 *)
PROG
(Magma) [ (3*4^n-0^n)/2: n in [0..22] ];
(PARI) a(n)=3*4^n\2 \\ Charles R Greathouse IV, Oct 12 2015
(Python) print([int(6*4**(n-1)) for n in range(50)]) # Karl V. Keller, Jr., Aug 30 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Klaus Brockhaus, Aug 31 2009
STATUS
approved