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,-9,2).
FORMULA
G.f.: (1-3*x^2+4*x^3) / ((1-2*x)*(1-4*x+x^2)).
From Colin Barker, Feb 04 2017: (Start)
a(n) = -2^n + 2*(2-sqrt(3))^n + 2*(2+sqrt(3))^n for n>0.
a(n) = 6*a(n-1) - 9*a(n-2) + 2*a(n-3) for n>3.
(End)
MATHEMATICA
Join[{1}, LinearRecurrence[{6, -9, 2}, {6, 24, 96}, 30]] (* Jean-François Alcover, Jan 09 2019 *)
PROG
(PARI) Vec((1-3*x^2+4*x^3) / ((1-2*x)*(1-4*x+x^2)) + O(x^30)) \\ Colin Barker, Feb 04 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane and Doron Zeilberger, Feb 19 2015
EXTENSIONS
Typo in the definition corrected by Antti Karttunen, Nov 18 2016
STATUS
approved