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A255284 a(n) = A255283(2^n-1). 2
1, 7, 31, 145, 601, 2551, 10351, 42433, 170761, 690247, 2768191, 11123185, 44543161, 178525591, 714455311, 2860291873, 11443638121, 45791846887, 183184681951, 732859788625, 2931560215321, 11727088287031, 46909200573871, 187642734275713, 750576869083081 (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 (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

Cf. A255283.

Sequence in context: A296573 A180147 A044049 * A005825 A086901 A003526

Adjacent sequences:  A255281 A255282 A255283 * A255285 A255286 A255287

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane and Doron Zeilberger, Feb 19 2015

STATUS

approved

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