A255442 a(n) = A255304(2^n-1).

1, 5, 15, 51, 153, 477, 1431, 4347, 13041, 39285, 117855, 354051, 1062153, 3187917, 9563751, 28695627, 86086881, 258273765, 774821295, 2324503251, 6973509753, 20920647357, 62761942071, 188286180507, 564858541521, 1694576687445, 5083730062335, 15251193375651, 45753580126953, 137260749946797

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 sequences related to cellular automata

Index entries for linear recurrences with constant coefficients, signature (3,3,-9).

Formula

G.f.: (1+3*x)*(1-x) / ((1-3*x)*(1-3*x^2)).

From Colin Barker, Feb 04 2017: (Start)

a(n) = 2*3^n - 3^((n-1)/2)/2*(1-(-1)^n+sqrt(3) + (-1)^n*sqrt(3)).

a(n) = 3*a(n-1) + 3*a(n-2) - 9*a(n-3) for n>2.

(End)

Mathematica

A255442[n_] := SeriesCoefficient[(1 + 3*x)*(1 - x)/((1 - 3*x)*(1 - 3*x^2)), {x, 0, n}]; Array[A255442, 30, 0] (* JungHwan Min, Sep 29 2016 *)
A255442L[n_] := CoefficientList[Series[(1 + 3*x)*(1 - x)/((1 - 3*x)*(1 - 3*x^2)), {x, 0, n}], x]; A255442L[29] (* JungHwan Min, Sep 29 2016 *)

Prog

(PARI) Vec((1+3*x)*(1-x) / ((1-3*x)*(1-3*x^2)) + O(x^30)) \\ Colin Barker, Feb 04 2017

Crossrefs

Cf. A255304.

Sequence in context: A363510 A120825 A199985 * A149576 A149577 A149578

Adjacent sequences: A255439 A255440 A255441 * A255443 A255444 A255445

Keyword

nonn,easy

Author

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

Status

approved