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 (6,-4,-16).
FORMULA
G.f.: (1-8*x^2-16*x^3) / ((1-4*x)*(1-2*x-4*x^2)).
From Colin Barker, Feb 05 2017: (Start)
a(n) = 4^n + (-(1-sqrt(5))^(1+n) + (1+sqrt(5))^(1+n)) / (2*sqrt(5)) for n>0.
a(n) = 6*a(n-1) - 4*a(n-2) - 16*a(n-3) for n>3.
(End)
PROG
(PARI) Vec((1-8*x^2-16*x^3) / ((1-4*x)*(1-2*x-4*x^2)) + O(x^30)) \\ Colin Barker, Feb 05 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane and Doron Zeilberger, Feb 23 2015
STATUS
approved