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 (4,7,-28).
FORMULA
G.f.: (1 - x)*(1 + 4*x) / ((1 - 4*x)*(1 - 7*x^2)).
From Colin Barker, Feb 04 2017: (Start)
a(n) = 2^(3+2*n)/3 - 7^((n-1)/2)/6*(11-11*(-1)^n + 5*sqrt(7) + 5*(-1)^n*sqrt(7)).
a(n) = 4*a(n-1) + 7*a(n-2) - 28*a(n-3) for n>2.
(End)
MATHEMATICA
LinearRecurrence[{4, 7, -28}, {1, 7, 31}, 30] (* Harvey P. Dale, Jul 20 2018 *)
PROG
(PARI) Vec((1 - x)*(1 + 4*x) / ((1 - 4*x)*(1 - 7*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
STATUS
approved