A255467 a(n) = A255466(2^n-1).

1, 6, 26, 110, 450, 1822, 7330, 29406, 117794, 471518, 1886754, 7548382, 30196258, 120790494, 483172898, 1932713438, 7730897442, 30923677150, 123694883362, 494779882974, 1979120230946, 7916482321886, 31665932083746, 126663733927390, 506654946894370, 2026619809947102, 8106479284527650, 32425917227589086

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,-2,-8).

Formula

G.f.: (1+2*x)*(1-x) / ((1-4*x)*(1-2*x)*(1+x)).

From Colin Barker, Feb 04 2017: (Start)

a(n) = (-2*(-1)^n/15 - 2^(1+n)/3 + (9*4^n)/5).

a(n) = 5*a(n-1) - 2*a(n-2) - 8*a(n-3) for n>2.

(End)

Mathematica

CoefficientList[Series[(1 + 2*x)*(1 - x)/((1 - 4*x)*(1 - 2*x)*(1 + x)), {x, 0, 30}], x] (* Wesley Ivan Hurt, Feb 04 2017 *)

Prog

(PARI) Vec((1+2*x)*(1-x) / ((1-4*x)*(1-2*x)*(1+x)) + O(x^30)) \\ Colin Barker, Feb 04 2017

Crossrefs

Cf. A255466.

Sequence in context: A079675 A113991 A267578 * A145374 A289789 A124465

Adjacent sequences: A255464 A255465 A255466 * A255468 A255469 A255470

Keyword

nonn,easy

Author

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

Status

approved