OFFSET
0,2
LINKS
Matthew House, Table of n, a(n) for n = 0..1803
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 (5,-6,2,4).
FORMULA
G.f.: (1 - x + 2*x^2 + 2*x^3)/((1 - 3*x - 2*x^2)*(1 - 2*x + 2*x^2)).
a(n) = 5*a(n-1) - 6*a(n-2) + 2*a(n-3) + 4*a(n-4). - Matthew House, Jan 15 2017
MATHEMATICA
A255303[n_] := SeriesCoefficient[(1 - x + 2*x^2 + 2*x^3)/((1 - 3*x - 2*x^2)*(1 - 2*x + 2*x^2)), {x, 0, n}]; Array[A255303, 28, 0] (* JungHwan Min, Sep 29 2016 *)
A255303L[n_] := CoefficientList[Series[(1 - x + 2*x^2 + 2*x^3)/((1 - 3*x - 2*x^2)*(1 - 2*x + 2*x^2)), {x, 0, n}], x]; A255303L[27] (* JungHwan Min, Sep 29 2016 *)
LinearRecurrence[{5, -6, 2, 4}, {1, 4, 16, 60}, 30] (* Harvey P. Dale, Feb 13 2022 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane and Doron Zeilberger, Feb 23 2015
STATUS
approved