OFFSET
0,2
LINKS
Colin Barker, 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,-1,-2,-4).
FORMULA
G.f.: (1-x)*(1+x+2*x^2) / (1-4*x+x^2+2*x^3+4*x^4).
a(n) = 4*a(n-1) - a(n-2) - 2*a(n-3) - 4*a(n-4) for n>3. - Colin Barker, Feb 04 2017
MATHEMATICA
LinearRecurrence[{4, -1, -2, -4}, {1, 4, 16, 56}, 30] (* Jean-François Alcover, Oct 10 2018 *)
PROG
(PARI) Vec((1-x)*(1+x+2*x^2) / (1-4*x+x^2+2*x^3+4*x^4) + O(x^30)) \\ Colin Barker, Feb 04 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane and Doron Zeilberger, Feb 23 2015
STATUS
approved