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A255296 a(n) = A255295(2^n-1). 2
1, 6, 24, 92, 340, 1236, 4452, 15956, 57028, 203508, 725604, 2585876, 9212932, 32818740, 116898468, 416365652, 1482959428, 5281740660, 18811402980, 66998214548, 238618498180, 849854020788, 3026803253028, 10780126189268, 38394001851076, 136742291486196 (list; graph; refs; listen; history; text; internal format)
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 (5,-4,-4).

FORMULA

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

From Colin Barker, Feb 03 2017: (Start)

a(n) = (2^(-n)*(-17*4^n + (17-5*sqrt(17))*(3-sqrt(17))^n + (3+sqrt(17))^n*(17+5*sqrt(17)))) / 17.

a(n) = 5*a(n-1) - 4*a(n-2) - 4*a(n-3) for n>2.

(End)

MATHEMATICA

A255296[n_] := SeriesCoefficient[-(2*t + 1)*(t - 1)/((-1 + 2*t)*(2*t^2 + 3*t - 1)), {t, 0, n}]; Array[A255296, 24, 0] (* JungHwan Min, Sep 29 2016 *)

A255296L[n_] := CoefficientList[Series[-(2*t + 1)*(t - 1)/((-1 + 2*t)*(2*t^2 + 3*t - 1)), {t, 0, n}], t]; A255296L[23] (* JungHwan Min, Sep 29 2016 *)

LinearRecurrence[{5, -4, -4}, {1, 6, 24}, 30] (* Vincenzo Librandi, Feb 04 2017 *)

PROG

(PARI) Vec((1-x)*(1+2*x) / ((1-2*x)*(1-3*x-2*x^2)) + O(x^30)) \\ Colin Barker, Feb 03 2017

(MAGMA) I:=[1, 6, 24]; [n le 3 select I[n] else 5*Self(n-1)-4*Self(n-2)-4*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 04 2017

CROSSREFS

Cf. A255295.

Sequence in context: A079839 A270955 A281074 * A242432 A255476 A303390

Adjacent sequences:  A255293 A255294 A255295 * A255297 A255298 A255299

KEYWORD

nonn,easy

AUTHOR

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

STATUS

approved

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Last modified March 23 18:13 EDT 2019. Contains 321433 sequences. (Running on oeis4.)