A255303 a(n) = A255302(2^n - 1).

1, 4, 16, 60, 216, 768, 2728, 9704, 34552, 123064, 438328, 1561176, 5560248, 19803096, 70529656, 251194904, 894643768, 3186321112, 11348251384, 40417397400, 143948695992, 512680882776, 1825940038264, 6503181876248, 23161425701176, 82490640856024, 293794773978616, 1046365603664280

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 sequences related to cellular automata

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

Cf. A255302.

Sequence in context: A089883 A089932 A120926 * A273347 A268939 A269635

Adjacent sequences: A255300 A255301 A255302 * A255304 A255305 A255306

Keyword

nonn

Author

N. J. A. Sloane and Doron Zeilberger, Feb 23 2015

Status

approved